{"id":1150,"date":"2015-03-16T13:28:09","date_gmt":"2015-03-16T18:28:09","guid":{"rendered":"https:\/\/blogs.mathworks.com\/loren\/?p=1150"},"modified":"2015-03-17T06:44:41","modified_gmt":"2015-03-17T11:44:41","slug":"the-ultimate-pi-day-is-over-now-what","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/loren\/2015\/03\/16\/the-ultimate-pi-day-is-over-now-what\/","title":{"rendered":"The Ultimate Pi Day is Over\u2026 Now What?"},"content":{"rendered":"\r\n\r\n<div class=\"content\"><!--introduction--><p>Today's post is from guest blogger Dan Seal who works in the MATLAB Product Marketing team here at MathWorks.  Dan recently celebrated Pi Day on 3\/14\/15 and wanted to know what other holidays he might be able to celebrate in the future.<\/p><!--\/introduction--><h3>Contents<\/h3><div><ul><li><a href=\"#00bf8317-119d-41db-8093-ee48508eafcd\">Starting small<\/a><\/li><li><a href=\"#cf7173ef-e438-4016-8302-c4793f336f5b\">Defining the possible date formats<\/a><\/li><li><a href=\"#31f538b5-5857-4f11-96ce-4dbd7c1dfbc8\">Extracting the digits<\/a><\/li><li><a href=\"#f4d124c7-f0ec-41aa-975e-9a9cc61a050b\">Building the list of special dates<\/a><\/li><li><a href=\"#b4c7dd40-fffb-4db1-89d7-9e08d30de9b3\">Printing out the results<\/a><\/li><li><a href=\"#ab1f2ecd-34f6-4084-b8f6-2c9496f9b73a\">Generalizing to a larger set of inputs<\/a><\/li><li><a href=\"#cbd3d377-62a1-46db-b057-0eb82070d055\">Now it's your turn<\/a><\/li><\/ul><\/div><p>Every year, mathematicians and their geeky cohort celebrate <a href=\"http:\/\/en.wikipedia.org\/wiki\/Pi_Day\">Pi Day<\/a> on the fourteenth of March, a date whose written representation (3\/14) looks like the first three digits of the mathematical constant pi (3.14).  But this year&#8217;s Pi Day was extra special and generated additional buzz because when you include the year in the written date of 3\/14\/15, it gives us two more digits of everyone&#8217;s favorite irrational number.  And if you were like me, you may have even marked the minute when it was 3\/14\/15 9:26, both in the AM and again in the PM.<\/p><p>But the opportunity to observe these additional digits of Pi on the calendar is something that comes around only once per century, so I don&#8217;t expect to see it again.  This got me wondering if there are any other special dates I might be able to look forward to.  M\/DD\/YY is not the only representation of a date, and Pi is not the only special constant out there with multiple digits.  So I collected all my favorite mathematical and physical constants along with a slew of possible date representations, and threw them all into MATLAB to see what it would give me.<\/p><h4>Starting small<a name=\"00bf8317-119d-41db-8093-ee48508eafcd\"><\/a><\/h4><p>I decided to start out with just two constants which I could use to test my work as I went along.  I selected Pi and the square root of 2. Fortunately, MATLAB can calculate a very accurate approximation of these values, so I didn&#8217;t have to look up the digits.<\/p><pre class=\"codeinput\">names = {\r\n    <span class=\"string\">'Archimedes'' Constant, or Pi'<\/span>\r\n    <span class=\"string\">'Pythagoras'' Constant, or Root 2'<\/span>\r\n    };\r\nnumbers = [\r\n    pi\r\n    sqrt(2)\r\n    ];\r\n<\/pre><h4>Defining the possible date formats<a name=\"cf7173ef-e438-4016-8302-c4793f336f5b\"><\/a><\/h4><p>Next, I wanted to construct all the allowable date formats.  I wanted to consider only dates that included the month, day, and year.  However, I figure it could be a 2- or 4-digit year.  Similarly, I allowed the month and day to each be 1 or 2 digits.  And finally, I allowed the month, day, and year to be ordered in any of four different arrangements:<\/p><div><ol><li>the American version of month\/day\/year,<\/li><li>the common standard outside the US, day\/month\/year,<\/li><li>the common year-first version, useful for sorting, year\/month\/day,<\/li><li>and for good measure, the alternate year-first arrangement, year\/day\/month.<\/li><\/ol><\/div><p>MATLAB uses the <a href=\"https:\/\/www.mathworks.com\/help\/matlab\/ref\/datetime.html\">datetime<\/a> data type, introduced in R2014b to easily manipulate and format dates and times.  Based on my formatting requirements above, I was able to build all the possible datetime format strings that would meet my criteria.<\/p><pre class=\"codeinput\">yearFormats  = {<span class=\"string\">'yy'<\/span> <span class=\"string\">'yyyy'<\/span>}; <span class=\"comment\">% 2 or 4 digit year<\/span>\r\nmonthFormats = {<span class=\"string\">'M'<\/span>  <span class=\"string\">'MM'<\/span>  }; <span class=\"comment\">% 1 or 2 digit month<\/span>\r\ndayFormats   = {<span class=\"string\">'d'<\/span>  <span class=\"string\">'dd'<\/span>  }; <span class=\"comment\">% 1 or 2 digit day<\/span>\r\n\r\navailableFormats{length(yearFormats)*length(monthFormats)*length(dayFormats)*4} = <span class=\"string\">''<\/span>;\r\nc = 1;\r\n<span class=\"keyword\">for<\/span> y = yearFormats\r\n    <span class=\"keyword\">for<\/span> m = monthFormats\r\n        <span class=\"keyword\">for<\/span> d = dayFormats\r\n            availableFormats{c  } = [d{:} <span class=\"string\">'\/'<\/span> m{:} <span class=\"string\">'\/'<\/span> y{:}];\r\n            availableFormats{c+1} = [m{:} <span class=\"string\">'\/'<\/span> d{:} <span class=\"string\">'\/'<\/span> y{:}];\r\n            availableFormats{c+2} = [y{:} <span class=\"string\">'\/'<\/span> m{:} <span class=\"string\">'\/'<\/span> d{:}];\r\n            availableFormats{c+3} = [y{:} <span class=\"string\">'\/'<\/span> d{:} <span class=\"string\">'\/'<\/span> m{:}];\r\n            c = c + 4;\r\n        <span class=\"keyword\">end<\/span>\r\n    <span class=\"keyword\">end<\/span>\r\n<span class=\"keyword\">end<\/span>\r\n\r\ndisp(availableFormats')\r\n<\/pre><pre class=\"codeoutput\">    'd\/M\/yy'\r\n    'M\/d\/yy'\r\n    'yy\/M\/d'\r\n    'yy\/d\/M'\r\n    'dd\/M\/yy'\r\n    'M\/dd\/yy'\r\n    'yy\/M\/dd'\r\n    'yy\/dd\/M'\r\n    'd\/MM\/yy'\r\n    'MM\/d\/yy'\r\n    'yy\/MM\/d'\r\n    'yy\/d\/MM'\r\n    'dd\/MM\/yy'\r\n    'MM\/dd\/yy'\r\n    'yy\/MM\/dd'\r\n    'yy\/dd\/MM'\r\n    'd\/M\/yyyy'\r\n    'M\/d\/yyyy'\r\n    'yyyy\/M\/d'\r\n    'yyyy\/d\/M'\r\n    'dd\/M\/yyyy'\r\n    'M\/dd\/yyyy'\r\n    'yyyy\/M\/dd'\r\n    'yyyy\/dd\/M'\r\n    'd\/MM\/yyyy'\r\n    'MM\/d\/yyyy'\r\n    'yyyy\/MM\/d'\r\n    'yyyy\/d\/MM'\r\n    'dd\/MM\/yyyy'\r\n    'MM\/dd\/yyyy'\r\n    'yyyy\/MM\/dd'\r\n    'yyyy\/dd\/MM'\r\n<\/pre><h4>Extracting the digits<a name=\"31f538b5-5857-4f11-96ce-4dbd7c1dfbc8\"><\/a><\/h4><p>The next task was to extract the digits from my numbers.  I figured I&#8217;d be using some quantities with large positive or negative exponents, so my technique had to be robust to different types of numbers.  I decided the best approach was to convert the numbers to strings using a consistent format so I could easily remove any decimal points and exponential terms. I found that <tt>sprintf<\/tt> with an exponential format could achieve this. Keeping nine digits after the decimal point ensured that I had enough precision to build even my longest date (which required 8 digits).  The <tt>char<\/tt> and <tt>arrayfun<\/tt> commands allowed me to run <tt>sprintf<\/tt> on each number individually and then build it into a character array.<\/p><pre class=\"codeinput\">digitsStr = char(arrayfun(@(x)sprintf(<span class=\"string\">'%1.9e'<\/span>,x),numbers,<span class=\"string\">'UniformOutput'<\/span>,false));\r\n\r\ndisp(digitsStr)\r\n<\/pre><pre class=\"codeoutput\">3.141592654e+00\r\n1.414213562e+00\r\n<\/pre><p>Next, I removed the decimal point and keep only the first eight digits, which is the most I will need.<\/p><pre class=\"codeinput\">digitsStr = digitsStr(:,[1 3:9]);\r\n\r\ndisp(digitsStr)\r\n<\/pre><pre class=\"codeoutput\">31415926\r\n14142135\r\n<\/pre><h4>Building the list of special dates<a name=\"f4d124c7-f0ec-41aa-975e-9a9cc61a050b\"><\/a><\/h4><p>Finally, I built a loop to test each of my mathematical constants against all the possible date formats and see which ones could be constructed as real dates.  I tried out each possible date format using a <tt>try\/catch<\/tt> statement.  If the date I tried to construct wasn&#8217;t a real date, I would catch that particular error.  But if it was, it would be added to the list of special holidays to celebrate and the name of that constant would be recorded as well.  I also specified a pivot year to define which century two-digit years belong to.  Since I&#8217;m looking or future holidays, I decided that all two-digit years should represent dates sometime after 2015.<\/p><pre class=\"codeinput\"><span class=\"comment\">% Initialize arrays<\/span>\r\nmaxPossibleDates = length(numbers)*length(availableFormats);\r\nholidayDates(maxPossibleDates) = datetime;\r\nholidayDates.Format = <span class=\"string\">'MMM dd, yyyy'<\/span>;\r\nholidayFormats{maxPossibleDates} = <span class=\"string\">''<\/span>;\r\nholidayNames{maxPossibleDates} = <span class=\"string\">''<\/span>;\r\n<span class=\"comment\">% Initialize counter<\/span>\r\nc = 1;\r\n<span class=\"keyword\">for<\/span> ii = 1:length(numbers) <span class=\"comment\">%Consider each number<\/span>\r\n    <span class=\"keyword\">for<\/span> jj = 1:length(availableFormats) <span class=\"comment\">%For each number, consider each format<\/span>\r\n        fmt = availableFormats{jj};\r\n        testFmt = strrep(fmt,<span class=\"string\">'\/'<\/span>,<span class=\"string\">''<\/span>);\r\n        strLength = length(testFmt);\r\n        testStr = digitsStr(ii,1:strLength);\r\n        <span class=\"keyword\">try<\/span> <span class=\"comment\">%If format is valid, add it to the list<\/span>\r\n            holidayDates(c) = datetime(testStr,<span class=\"string\">'InputFormat'<\/span>,testFmt,<span class=\"string\">'PivotYear'<\/span>,2015);\r\n            holidayFormats{c} = fmt;\r\n            holidayNames{c} = names{ii};\r\n            c = c + 1;\r\n        <span class=\"keyword\">catch<\/span> err <span class=\"comment\">%If format errors, make sure it is the expected error<\/span>\r\n            <span class=\"keyword\">if<\/span> ~strcmp(err.identifier,<span class=\"string\">'MATLAB:datetime:ParseErr'<\/span>)\r\n                rethrow(err)\r\n            <span class=\"keyword\">end<\/span>\r\n        <span class=\"keyword\">end<\/span>\r\n    <span class=\"keyword\">end<\/span>\r\n<span class=\"keyword\">end<\/span>\r\n<span class=\"comment\">% Trim empty values from end of lists<\/span>\r\nholidayDates = holidayDates(1:c-1);\r\nholidayFormats = holidayFormats(1:c-1);\r\nholidayNames = holidayNames(1:c-1);\r\n<\/pre><p>Because my dates are represented as datetimes, I can easily put them in chronological order with the <tt>sort<\/tt> function.<\/p><pre class=\"codeinput\">[holidayDates,ind] = sort(holidayDates);\r\nholidayFormats = holidayFormats(ind);\r\nholidayNames = holidayNames(ind);\r\n<\/pre><h4>Printing out the results<a name=\"b4c7dd40-fffb-4db1-89d7-9e08d30de9b3\"><\/a><\/h4><p>Let&#8217;s see how many opportunities there are to celebrate Pi Day or Root 2 Day.<\/p><pre class=\"codeinput\"><span class=\"keyword\">for<\/span> ii = 1:c-1\r\n    specialDate = holidayDates(ii);\r\n    specialDate.Format = holidayFormats{ii};\r\n    fprintf(<span class=\"string\">'On %s (%s), we can celebrate %s Day\\n'<\/span>,<span class=\"keyword\">...<\/span>\r\n        char(holidayDates(ii)),char(specialDate),holidayNames{ii})\r\n<span class=\"keyword\">end<\/span>\r\n<\/pre><p>It looks like there are a few Pi Days we can celebrate over the next 30 years.  And then there are some Root 2 Days to celebrate after that.<\/p><pre class=\"codeoutput\">On Jan 02, 1414 (1414\/2\/1), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Feb 01, 1414 (1414\/2\/1), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Feb 13, 1414 (1414\/2\/13), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Mar 21, 1414 (1414\/21\/3), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Jan 04, 1421 (1\/4\/1421), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Apr 01, 1421 (1\/4\/1421), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Mar 14, 1592 (3\/14\/1592), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Mar 14, 2015 (3\/14\/15), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 04, 2031 (31\/4\/1), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Apr 01, 2031 (31\/4\/1), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Apr 15, 2031 (31\/4\/15), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 03, 2041 (3\/1\/41), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Mar 01, 2041 (3\/1\/41), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 14, 2042 (14\/1\/42), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Jan 04, 2114 (1\/4\/14), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Jan 04, 2114 (14\/1\/4), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Feb 14, 2114 (14\/14\/2), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Apr 01, 2114 (1\/4\/14), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Apr 01, 2114 (14\/1\/4), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn May 09, 3141 (3141\/5\/9), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Sep 05, 3141 (3141\/5\/9), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 03, 4159 (3\/1\/4159), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Mar 01, 4159 (3\/1\/4159), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 14, 4213 (14\/1\/4213), we can celebrate Pythagoras' Constant, or Root 2 Day\r\n<\/pre><h4>Generalizing to a larger set of inputs<a name=\"ab1f2ecd-34f6-4084-b8f6-2c9496f9b73a\"><\/a><\/h4><p>Since this gave me good results, I could put the entire analysis into a function and then call it with a much longer list of my favorite <a href=\"http:\/\/en.wikipedia.org\/wiki\/Mathematical_constant\">mathematical<\/a> and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Physical_constant\">physical<\/a> constants. What are the next holidays coming up?  Be sure to mark your calendar.<\/p><pre class=\"codeinput\">names = {\r\n    <span class=\"string\">'Archimedes'' Constant, or Pi'<\/span>\r\n    <span class=\"string\">'Euler''s Number, or e'<\/span>\r\n    <span class=\"string\">'Pythagoras'' Constant, or Root 2'<\/span>\r\n    <span class=\"string\">'Golden Ratio, or Phi'<\/span>\r\n    <span class=\"string\">'Root 3'<\/span>\r\n    <span class=\"string\">'Root 5'<\/span>\r\n    <span class=\"string\">'Speed of Light, or c'<\/span>\r\n    <span class=\"string\">'Avogadro''s Number, or N_A'<\/span>\r\n    <span class=\"string\">'Standard Gravity, or g'<\/span>\r\n    <span class=\"string\">'Gravitational Constant, or G'<\/span>\r\n    <span class=\"string\">'Planck Constant, or h'<\/span>\r\n    <span class=\"string\">'Ideal Gas Constant, or R'<\/span>\r\n    <span class=\"string\">'Coulomb''s Constant, or k_e'<\/span>\r\n    <span class=\"string\">'Elementary Charge, or e'<\/span>\r\n    <span class=\"string\">'Bohr Radius, or a_0'<\/span>\r\n    <span class=\"string\">'Electron Mass, or m_e'<\/span>\r\n    <span class=\"string\">'Proton Mass, or m_p'<\/span>\r\n    <span class=\"string\">'Atomic Mass Constant, or m_u'<\/span>\r\n    <span class=\"string\">'Boltzmann Constant, or k_B'<\/span>\r\n    <span class=\"string\">'Faraday Constant, or F'<\/span>\r\n    <span class=\"string\">'Stefan-Boltzmann Constant, or Theta'<\/span>\r\n    <span class=\"string\">'Standard Atmosphere, or atm'<\/span>\r\n    <span class=\"string\">'Planck Length, or l_P'<\/span>\r\n    <span class=\"string\">'Planck Mass, or m_P'<\/span>\r\n    <span class=\"string\">'Planck Time, or t_P'<\/span>\r\n    <span class=\"string\">'Planck Charge, or q_P'<\/span>\r\n    <span class=\"string\">'Planck Temperature, or T_P'<\/span>\r\n    };\r\nnumbers = [\r\n    pi\r\n    exp(1)\r\n    sqrt(2)\r\n    (1+sqrt(5))\/2\r\n    sqrt(3)\r\n    sqrt(5)\r\n    299792458\r\n    6.02214129e23\r\n    9.80665\r\n    6.67384e-11\r\n    6.62606957e-34\r\n    8.3144621\r\n    8.9875517873681764e9\r\n    1.602176565e-19\r\n    5.2917721092e-11\r\n    9.10938291e-31\r\n    1.672621777e-27\r\n    1.660538921e-27\r\n    1.3806488e-23\r\n    96485.3365\r\n    5.670373e-8\r\n    101325\r\n    1.616199e-35\r\n    2.17651e-8\r\n    5.39106e-44\r\n    1.875545956e-18\r\n    1.416833e32\r\n    ];\r\n\r\nholidayForFamousConstants(numbers,names)\r\n<\/pre><pre class=\"codeoutput\">On Jan 06, 0217 (1\/6\/0217), we can celebrate Elementary Charge, or e Day\r\nOn Jun 01, 0217 (1\/6\/0217), we can celebrate Elementary Charge, or e Day\r\nOn Jun 16, 0538 (16\/6\/0538), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Aug 13, 0648 (13\/8\/0648), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Aug 09, 0665 (9\/8\/0665), we can celebrate Standard Gravity, or g Day\r\nOn Sep 08, 0665 (9\/8\/0665), we can celebrate Standard Gravity, or g Day\r\nOn Jan 09, 0938 (9\/1\/0938), we can celebrate Electron Mass, or m_e Day\r\nOn Sep 01, 0938 (9\/1\/0938), we can celebrate Electron Mass, or m_e Day\r\nOn Feb 05, 1013 (1013\/2\/5), we can celebrate Standard Atmosphere, or atm Day\r\nOn May 02, 1013 (1013\/2\/5), we can celebrate Standard Atmosphere, or atm Day\r\nOn Apr 06, 1380 (1380\/6\/4), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Jun 04, 1380 (1380\/6\/4), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Jan 02, 1414 (1414\/2\/1), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Feb 01, 1414 (1414\/2\/1), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Feb 13, 1414 (1414\/2\/13), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Mar 21, 1414 (1414\/21\/3), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Mar 08, 1416 (1416\/8\/3), we can celebrate Planck Temperature, or T_P Day\r\nOn Aug 03, 1416 (1416\/8\/3), we can celebrate Planck Temperature, or T_P Day\r\nOn Jan 04, 1421 (1\/4\/1421), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Apr 01, 1421 (1\/4\/1421), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Mar 08, 1446 (8\/3\/1446), we can celebrate Ideal Gas Constant, or R Day\r\nOn Aug 03, 1446 (8\/3\/1446), we can celebrate Ideal Gas Constant, or R Day\r\nOn Mar 14, 1592 (3\/14\/1592), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 07, 1602 (1602\/1\/7), we can celebrate Elementary Charge, or e Day\r\nOn Jun 17, 1602 (1602\/17\/6), we can celebrate Elementary Charge, or e Day\r\nOn Jul 01, 1602 (1602\/1\/7), we can celebrate Elementary Charge, or e Day\r\nOn Jan 09, 1616 (1616\/1\/9), we can celebrate Planck Length, or l_P Day\r\nOn Sep 01, 1616 (1616\/1\/9), we can celebrate Planck Length, or l_P Day\r\nOn Sep 19, 1616 (1616\/19\/9), we can celebrate Planck Length, or l_P Day\r\nOn Mar 03, 1618 (1618\/03\/3), we can celebrate Golden Ratio, or Phi Day\r\nOn Mar 03, 1618 (1618\/03\/3), we can celebrate Golden Ratio, or Phi Day\r\nOn Jan 06, 1619 (1\/6\/1619), we can celebrate Planck Length, or l_P Day\r\nOn Jun 01, 1619 (1\/6\/1619), we can celebrate Planck Length, or l_P Day\r\nOn Mar 05, 1660 (1660\/5\/3), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn May 03, 1660 (1660\/5\/3), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Feb 06, 1672 (1672\/6\/2), we can celebrate Proton Mass, or m_p Day\r\nOn Jun 02, 1672 (1672\/6\/2), we can celebrate Proton Mass, or m_p Day\r\nOn Jun 21, 1672 (1672\/6\/21), we can celebrate Proton Mass, or m_p Day\r\nOn Jan 04, 1683 (1\/4\/1683), we can celebrate Planck Temperature, or T_P Day\r\nOn Apr 01, 1683 (1\/4\/1683), we can celebrate Planck Temperature, or T_P Day\r\nOn May 08, 1732 (1732\/05\/08), we can celebrate Root 3 Day\r\nOn Aug 05, 1732 (1732\/05\/08), we can celebrate Root 3 Day\r\nOn Feb 16, 1765 (16\/02\/1765), we can celebrate Elementary Charge, or e Day\r\nOn May 29, 1772 (5\/29\/1772), we can celebrate Bohr Radius, or a_0 Day\r\nOn Jan 06, 1803 (1\/6\/1803), we can celebrate Golden Ratio, or Phi Day\r\nOn Jun 01, 1803 (1\/6\/1803), we can celebrate Golden Ratio, or Phi Day\r\nOn Feb 07, 1828 (2\/7\/1828), we can celebrate Euler's Number, or e Day\r\nOn Jul 02, 1828 (2\/7\/1828), we can celebrate Euler's Number, or e Day\r\nOn Apr 05, 1875 (1875\/5\/4), we can celebrate Planck Charge, or q_P Day\r\nOn May 04, 1875 (1875\/5\/4), we can celebrate Planck Charge, or q_P Day\r\nOn Mar 14, 2015 (3\/14\/15), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 02, 2016 (16\/02\/1), we can celebrate Elementary Charge, or e Day\r\nOn Jan 04, 2016 (1\/4\/16), we can celebrate Planck Temperature, or T_P Day\r\nOn Jan 06, 2016 (1\/6\/16), we can celebrate Planck Length, or l_P Day\r\nOn Jan 06, 2016 (16\/1\/6), we can celebrate Planck Length, or l_P Day\r\nOn Jan 08, 2016 (16\/1\/8), we can celebrate Golden Ratio, or Phi Day\r\nOn Jan 16, 2016 (16\/16\/1), we can celebrate Planck Length, or l_P Day\r\nOn Feb 01, 2016 (16\/02\/1), we can celebrate Elementary Charge, or e Day\r\nOn Feb 07, 2016 (16\/7\/2), we can celebrate Proton Mass, or m_p Day\r\nOn Feb 17, 2016 (16\/02\/17), we can celebrate Elementary Charge, or e Day\r\nOn Mar 18, 2016 (16\/18\/03), we can celebrate Golden Ratio, or Phi Day\r\nOn Apr 01, 2016 (1\/4\/16), we can celebrate Planck Temperature, or T_P Day\r\nOn May 06, 2016 (16\/6\/05), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Jun 01, 2016 (1\/6\/16), we can celebrate Planck Length, or l_P Day\r\nOn Jun 01, 2016 (16\/1\/6), we can celebrate Planck Length, or l_P Day\r\nOn Jun 05, 2016 (16\/6\/05), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Jul 02, 2016 (16\/7\/2), we can celebrate Proton Mass, or m_p Day\r\nOn Jul 26, 2016 (16\/7\/26), we can celebrate Proton Mass, or m_p Day\r\nOn Aug 01, 2016 (16\/1\/8), we can celebrate Golden Ratio, or Phi Day\r\nOn Feb 03, 2017 (17\/3\/2), we can celebrate Root 3 Day\r\nOn Feb 16, 2017 (16\/02\/17), we can celebrate Elementary Charge, or e Day\r\nOn Mar 02, 2017 (17\/3\/2), we can celebrate Root 3 Day\r\nOn Mar 20, 2017 (17\/3\/20), we can celebrate Root 3 Day\r\nOn May 29, 2017 (5\/29\/17), we can celebrate Bohr Radius, or a_0 Day\r\nOn Jan 06, 2018 (1\/6\/18), we can celebrate Golden Ratio, or Phi Day\r\nOn Feb 07, 2018 (2\/7\/18), we can celebrate Euler's Number, or e Day\r\nOn May 07, 2018 (18\/7\/5), we can celebrate Planck Charge, or q_P Day\r\nOn Jun 01, 2018 (1\/6\/18), we can celebrate Golden Ratio, or Phi Day\r\nOn Jul 02, 2018 (2\/7\/18), we can celebrate Euler's Number, or e Day\r\nOn Jul 05, 2018 (18\/7\/5), we can celebrate Planck Charge, or q_P Day\r\nOn Mar 17, 2020 (17\/3\/20), we can celebrate Root 3 Day\r\nOn Feb 06, 2021 (6\/02\/21), we can celebrate Avogadro's Number, or N_A Day\r\nOn Jun 02, 2021 (6\/02\/21), we can celebrate Avogadro's Number, or N_A Day\r\nOn Jun 07, 2021 (21\/7\/6), we can celebrate Planck Mass, or m_P Day\r\nOn Jul 06, 2021 (21\/7\/6), we can celebrate Planck Mass, or m_P Day\r\nOn Mar 06, 2022 (22\/3\/6), we can celebrate Root 5 Day\r\nOn Jun 03, 2022 (22\/3\/6), we can celebrate Root 5 Day\r\nOn Oct 13, 2025 (10\/13\/25), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jun 06, 2026 (6\/6\/26), we can celebrate Planck Constant, or h Day\r\nOn Jun 06, 2026 (6\/6\/26), we can celebrate Planck Constant, or h Day\r\nOn Jul 16, 2026 (16\/7\/26), we can celebrate Proton Mass, or m_p Day\r\nOn Jan 08, 2027 (27\/1\/8), we can celebrate Euler's Number, or e Day\r\nOn Feb 18, 2027 (27\/18\/2), we can celebrate Euler's Number, or e Day\r\nOn Aug 01, 2027 (27\/1\/8), we can celebrate Euler's Number, or e Day\r\nOn Jul 09, 2029 (29\/9\/7), we can celebrate Speed of Light, or c Day\r\nOn Sep 07, 2029 (29\/9\/7), we can celebrate Speed of Light, or c Day\r\nOn Jan 04, 2031 (31\/4\/1), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Apr 01, 2031 (31\/4\/1), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Apr 15, 2031 (31\/4\/15), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 01, 2032 (1\/01\/32), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jan 01, 2032 (1\/01\/32), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jan 07, 2032 (1\/7\/32), we can celebrate Root 3 Day\r\nOn Jan 10, 2032 (10\/1\/32), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jul 01, 2032 (1\/7\/32), we can celebrate Root 3 Day\r\nOn Oct 01, 2032 (10\/1\/32), we can celebrate Standard Atmosphere, or atm Day\r\nOn Feb 02, 2036 (2\/2\/36), we can celebrate Root 5 Day\r\nOn Feb 02, 2036 (2\/2\/36), we can celebrate Root 5 Day\r\nOn Jan 03, 2041 (3\/1\/41), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Mar 01, 2041 (3\/1\/41), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 14, 2042 (14\/1\/42), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Aug 31, 2044 (8\/31\/44), we can celebrate Ideal Gas Constant, or R Day\r\nOn Jun 09, 2048 (9\/6\/48), we can celebrate Faraday Constant, or F Day\r\nOn Sep 06, 2048 (9\/6\/48), we can celebrate Faraday Constant, or F Day\r\nOn Mar 17, 2050 (17\/3\/2050), we can celebrate Root 3 Day\r\nOn Jan 09, 2052 (52\/9\/1), we can celebrate Bohr Radius, or a_0 Day\r\nOn Sep 01, 2052 (52\/9\/1), we can celebrate Bohr Radius, or a_0 Day\r\nOn Sep 17, 2052 (52\/9\/17), we can celebrate Bohr Radius, or a_0 Day\r\nOn Jan 09, 2053 (53\/9\/1), we can celebrate Planck Time, or t_P Day\r\nOn Sep 01, 2053 (53\/9\/1), we can celebrate Planck Time, or t_P Day\r\nOn Sep 10, 2053 (53\/9\/10), we can celebrate Planck Time, or t_P Day\r\nOn Oct 09, 2053 (53\/9\/10), we can celebrate Planck Time, or t_P Day\r\nOn Jul 18, 2055 (18\/7\/55), we can celebrate Planck Charge, or q_P Day\r\nOn Mar 07, 2056 (56\/7\/03), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jul 03, 2056 (56\/7\/03), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jan 06, 2060 (1\/6\/60), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Jan 22, 2060 (60\/22\/1), we can celebrate Avogadro's Number, or N_A Day\r\nOn Feb 02, 2060 (60\/2\/2), we can celebrate Avogadro's Number, or N_A Day\r\nOn Feb 02, 2060 (60\/2\/2), we can celebrate Avogadro's Number, or N_A Day\r\nOn Feb 21, 2060 (60\/2\/21), we can celebrate Avogadro's Number, or N_A Day\r\nOn Feb 23, 2060 (2\/23\/60), we can celebrate Root 5 Day\r\nOn Mar 22, 2060 (22\/3\/60), we can celebrate Root 5 Day\r\nOn Jun 01, 2060 (1\/6\/60), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Jan 16, 2061 (16\/1\/61), we can celebrate Planck Length, or l_P Day\r\nOn Feb 17, 2065 (2\/17\/65), we can celebrate Planck Mass, or m_P Day\r\nOn Jul 21, 2065 (21\/7\/65), we can celebrate Planck Mass, or m_P Day\r\nOn Feb 06, 2066 (66\/2\/6), we can celebrate Planck Constant, or h Day\r\nOn Mar 07, 2066 (66\/7\/3), we can celebrate Gravitational Constant, or G Day\r\nOn Jun 02, 2066 (66\/2\/6), we can celebrate Planck Constant, or h Day\r\nOn Jun 26, 2066 (66\/26\/06), we can celebrate Planck Constant, or h Day\r\nOn Jul 03, 2066 (66\/7\/3), we can celebrate Gravitational Constant, or G Day\r\nOn Jan 14, 2068 (14\/1\/68), we can celebrate Planck Temperature, or T_P Day\r\nOn May 06, 2070 (5\/6\/70), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jun 05, 2070 (5\/6\/70), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jan 06, 2072 (1\/6\/72), we can celebrate Proton Mass, or m_p Day\r\nOn Jun 01, 2072 (1\/6\/72), we can celebrate Proton Mass, or m_p Day\r\nOn Jun 06, 2073 (6\/6\/73), we can celebrate Gravitational Constant, or G Day\r\nOn Jun 06, 2073 (6\/6\/73), we can celebrate Gravitational Constant, or G Day\r\nOn Jan 08, 2075 (1\/8\/75), we can celebrate Planck Charge, or q_P Day\r\nOn Aug 01, 2075 (1\/8\/75), we can celebrate Planck Charge, or q_P Day\r\nOn Jan 02, 2076 (2\/1\/76), we can celebrate Planck Mass, or m_P Day\r\nOn Feb 01, 2076 (2\/1\/76), we can celebrate Planck Mass, or m_P Day\r\nOn Sep 29, 2079 (29\/9\/79), we can celebrate Speed of Light, or c Day\r\nOn Jan 03, 2080 (1\/3\/80), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Jan 16, 2080 (16\/1\/80), we can celebrate Golden Ratio, or Phi Day\r\nOn Mar 01, 2080 (1\/3\/80), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Jan 27, 2082 (27\/1\/82), we can celebrate Euler's Number, or e Day\r\nOn Jan 04, 2083 (83\/1\/4), we can celebrate Ideal Gas Constant, or R Day\r\nOn Apr 01, 2083 (83\/1\/4), we can celebrate Ideal Gas Constant, or R Day\r\nOn Apr 14, 2083 (83\/14\/4), we can celebrate Ideal Gas Constant, or R Day\r\nOn Aug 09, 2087 (8\/9\/87), we can celebrate Coulomb's Constant, or k_e Day\r\nOn Sep 08, 2087 (8\/9\/87), we can celebrate Coulomb's Constant, or k_e Day\r\nOn Jul 08, 2089 (89\/8\/7), we can celebrate Coulomb's Constant, or k_e Day\r\nOn Aug 07, 2089 (89\/8\/7), we can celebrate Coulomb's Constant, or k_e Day\r\nOn Feb 05, 2091 (5\/2\/91), we can celebrate Bohr Radius, or a_0 Day\r\nOn Mar 05, 2091 (5\/3\/91), we can celebrate Planck Time, or t_P Day\r\nOn Mar 09, 2091 (91\/09\/3), we can celebrate Electron Mass, or m_e Day\r\nOn May 02, 2091 (5\/2\/91), we can celebrate Bohr Radius, or a_0 Day\r\nOn May 03, 2091 (5\/3\/91), we can celebrate Planck Time, or t_P Day\r\nOn Sep 03, 2091 (91\/09\/3), we can celebrate Electron Mass, or m_e Day\r\nOn Sep 10, 2093 (9\/10\/93), we can celebrate Electron Mass, or m_e Day\r\nOn Oct 09, 2093 (9\/10\/93), we can celebrate Electron Mass, or m_e Day\r\nOn Apr 08, 2096 (96\/4\/8), we can celebrate Faraday Constant, or F Day\r\nOn Aug 04, 2096 (96\/4\/8), we can celebrate Faraday Constant, or F Day\r\nOn Feb 09, 2097 (2\/9\/97), we can celebrate Speed of Light, or c Day\r\nOn Sep 02, 2097 (2\/9\/97), we can celebrate Speed of Light, or c Day\r\nOn Jun 06, 2098 (98\/06\/6), we can celebrate Standard Gravity, or g Day\r\nOn Jun 06, 2098 (98\/06\/6), we can celebrate Standard Gravity, or g Day\r\nOn Jan 06, 2102 (1\/6\/02), we can celebrate Elementary Charge, or e Day\r\nOn Jun 01, 2102 (1\/6\/02), we can celebrate Elementary Charge, or e Day\r\nOn Jun 16, 2105 (16\/6\/05), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Aug 09, 2106 (9\/8\/06), we can celebrate Standard Gravity, or g Day\r\nOn Aug 13, 2106 (13\/8\/06), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Sep 08, 2106 (9\/8\/06), we can celebrate Standard Gravity, or g Day\r\nOn Jan 09, 2109 (9\/1\/09), we can celebrate Electron Mass, or m_e Day\r\nOn Sep 01, 2109 (9\/1\/09), we can celebrate Electron Mass, or m_e Day\r\nOn Jan 03, 2110 (10\/1\/3), we can celebrate Standard Atmosphere, or atm Day\r\nOn Feb 13, 2110 (10\/13\/2), we can celebrate Standard Atmosphere, or atm Day\r\nOn Mar 01, 2110 (10\/1\/3), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jun 08, 2113 (13\/8\/06), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Aug 06, 2113 (13\/8\/06), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Jan 04, 2114 (1\/4\/14), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Jan 04, 2114 (14\/1\/4), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Jan 06, 2114 (14\/1\/6), we can celebrate Planck Temperature, or T_P Day\r\nOn Feb 14, 2114 (14\/14\/2), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Mar 08, 2114 (8\/3\/14), we can celebrate Ideal Gas Constant, or R Day\r\nOn Apr 01, 2114 (1\/4\/14), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Apr 01, 2114 (14\/1\/4), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Jun 01, 2114 (14\/1\/6), we can celebrate Planck Temperature, or T_P Day\r\nOn Aug 03, 2114 (8\/3\/14), we can celebrate Ideal Gas Constant, or R Day\r\nOn Aug 16, 2114 (14\/16\/8), we can celebrate Planck Temperature, or T_P Day\r\nOn Feb 06, 2141 (6\/02\/2141), we can celebrate Avogadro's Number, or N_A Day\r\nOn Jun 02, 2141 (6\/02\/2141), we can celebrate Avogadro's Number, or N_A Day\r\nOn Jan 05, 2176 (2176\/5\/1), we can celebrate Planck Mass, or m_P Day\r\nOn May 01, 2176 (2176\/5\/1), we can celebrate Planck Mass, or m_P Day\r\nOn May 10, 2176 (2176\/5\/10), we can celebrate Planck Mass, or m_P Day\r\nOn Oct 05, 2176 (2176\/5\/10), we can celebrate Planck Mass, or m_P Day\r\nOn Jun 07, 2236 (2236\/06\/7), we can celebrate Root 5 Day\r\nOn Jul 06, 2236 (2236\/06\/7), we can celebrate Root 5 Day\r\nOn Oct 13, 2500 (10\/13\/2500), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jun 06, 2606 (6\/6\/2606), we can celebrate Planck Constant, or h Day\r\nOn Jun 06, 2606 (6\/6\/2606), we can celebrate Planck Constant, or h Day\r\nOn Jul 16, 2621 (16\/7\/2621), we can celebrate Proton Mass, or m_p Day\r\nOn Jan 28, 2718 (2718\/28\/1), we can celebrate Euler's Number, or e Day\r\nOn Feb 08, 2718 (2718\/2\/8), we can celebrate Euler's Number, or e Day\r\nOn Aug 02, 2718 (2718\/2\/8), we can celebrate Euler's Number, or e Day\r\nOn Feb 09, 2997 (2997\/9\/2), we can celebrate Speed of Light, or c Day\r\nOn Sep 02, 2997 (2997\/9\/2), we can celebrate Speed of Light, or c Day\r\nOn Sep 24, 2997 (2997\/9\/24), we can celebrate Speed of Light, or c Day\r\nOn May 09, 3141 (3141\/5\/9), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Sep 05, 3141 (3141\/5\/9), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 07, 3205 (1\/7\/3205), we can celebrate Root 3 Day\r\nOn Jul 01, 3205 (1\/7\/3205), we can celebrate Root 3 Day\r\nOn Jan 01, 3250 (1\/01\/3250), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jan 01, 3250 (1\/01\/3250), we can celebrate Standard Atmosphere, or atm Day\r\nOn Jan 10, 3250 (10\/1\/3250), we can celebrate Standard Atmosphere, or atm Day\r\nOn Oct 01, 3250 (10\/1\/3250), we can celebrate Standard Atmosphere, or atm Day\r\nOn Feb 02, 3606 (2\/2\/3606), we can celebrate Root 5 Day\r\nOn Feb 02, 3606 (2\/2\/3606), we can celebrate Root 5 Day\r\nOn Jan 03, 4159 (3\/1\/4159), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Mar 01, 4159 (3\/1\/4159), we can celebrate Archimedes' Constant, or Pi Day\r\nOn Jan 14, 4213 (14\/1\/4213), we can celebrate Pythagoras' Constant, or Root 2 Day\r\nOn Aug 31, 4462 (8\/31\/4462), we can celebrate Ideal Gas Constant, or R Day\r\nOn Jun 09, 4853 (9\/6\/4853), we can celebrate Faraday Constant, or F Day\r\nOn Sep 06, 4853 (9\/6\/4853), we can celebrate Faraday Constant, or F Day\r\nOn Jul 07, 5291 (5291\/7\/7), we can celebrate Bohr Radius, or a_0 Day\r\nOn Jul 07, 5291 (5291\/7\/7), we can celebrate Bohr Radius, or a_0 Day\r\nOn Jul 18, 5545 (18\/7\/5545), we can celebrate Planck Charge, or q_P Day\r\nOn Mar 07, 5670 (5670\/3\/7), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jul 03, 5670 (5670\/3\/7), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jan 04, 6022 (6022\/1\/4), we can celebrate Avogadro's Number, or N_A Day\r\nOn Jan 14, 6022 (6022\/14\/1), we can celebrate Avogadro's Number, or N_A Day\r\nOn Apr 01, 6022 (6022\/1\/4), we can celebrate Avogadro's Number, or N_A Day\r\nOn Dec 14, 6022 (6022\/14\/12), we can celebrate Avogadro's Number, or N_A Day\r\nOn Jan 06, 6053 (1\/6\/6053), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Jun 01, 6053 (1\/6\/6053), we can celebrate Atomic Mass Constant, or m_u Day\r\nOn Feb 23, 6067 (2\/23\/6067), we can celebrate Root 5 Day\r\nOn Mar 22, 6067 (22\/3\/6067), we can celebrate Root 5 Day\r\nOn Jan 16, 6199 (16\/1\/6199), we can celebrate Planck Length, or l_P Day\r\nOn Feb 17, 6510 (2\/17\/6510), we can celebrate Planck Mass, or m_P Day\r\nOn Jul 21, 6510 (21\/7\/6510), we can celebrate Planck Mass, or m_P Day\r\nOn Jun 09, 6626 (6626\/06\/9), we can celebrate Planck Constant, or h Day\r\nOn Sep 06, 6626 (6626\/06\/9), we can celebrate Planck Constant, or h Day\r\nOn Apr 08, 6673 (6673\/8\/4), we can celebrate Gravitational Constant, or G Day\r\nOn Aug 04, 6673 (6673\/8\/4), we can celebrate Gravitational Constant, or G Day\r\nOn Jan 14, 6833 (14\/1\/6833), we can celebrate Planck Temperature, or T_P Day\r\nOn May 06, 7037 (5\/6\/7037), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jun 05, 7037 (5\/6\/7037), we can celebrate Stefan-Boltzmann Constant, or Theta Day\r\nOn Jan 06, 7262 (1\/6\/7262), we can celebrate Proton Mass, or m_p Day\r\nOn Jun 01, 7262 (1\/6\/7262), we can celebrate Proton Mass, or m_p Day\r\nOn Jun 06, 7384 (6\/6\/7384), we can celebrate Gravitational Constant, or G Day\r\nOn Jun 06, 7384 (6\/6\/7384), we can celebrate Gravitational Constant, or G Day\r\nOn Jan 08, 7554 (1\/8\/7554), we can celebrate Planck Charge, or q_P Day\r\nOn Aug 01, 7554 (1\/8\/7554), we can celebrate Planck Charge, or q_P Day\r\nOn Jan 02, 7651 (2\/1\/7651), we can celebrate Planck Mass, or m_P Day\r\nOn Feb 01, 7651 (2\/1\/7651), we can celebrate Planck Mass, or m_P Day\r\nOn Sep 29, 7924 (29\/9\/7924), we can celebrate Speed of Light, or c Day\r\nOn Jan 16, 8033 (16\/1\/8033), we can celebrate Golden Ratio, or Phi Day\r\nOn Jan 03, 8064 (1\/3\/8064), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Mar 01, 8064 (1\/3\/8064), we can celebrate Boltzmann Constant, or k_B Day\r\nOn Jan 27, 8281 (27\/1\/8281), we can celebrate Euler's Number, or e Day\r\nOn Apr 06, 8314 (8314\/4\/6), we can celebrate Ideal Gas Constant, or R Day\r\nOn Jun 04, 8314 (8314\/4\/6), we can celebrate Ideal Gas Constant, or R Day\r\nOn Aug 09, 8755 (8\/9\/8755), we can celebrate Coulomb's Constant, or k_e Day\r\nOn Sep 08, 8755 (8\/9\/8755), we can celebrate Coulomb's Constant, or k_e Day\r\nOn May 05, 8987 (8987\/5\/5), we can celebrate Coulomb's Constant, or k_e Day\r\nOn May 05, 8987 (8987\/5\/5), we can celebrate Coulomb's Constant, or k_e Day\r\nOn Mar 05, 9106 (5\/3\/9106), we can celebrate Planck Time, or t_P Day\r\nOn May 03, 9106 (5\/3\/9106), we can celebrate Planck Time, or t_P Day\r\nOn Mar 08, 9109 (9109\/3\/8), we can celebrate Electron Mass, or m_e Day\r\nOn Aug 03, 9109 (9109\/3\/8), we can celebrate Electron Mass, or m_e Day\r\nOn Feb 05, 9177 (5\/2\/9177), we can celebrate Bohr Radius, or a_0 Day\r\nOn May 02, 9177 (5\/2\/9177), we can celebrate Bohr Radius, or a_0 Day\r\nOn Sep 10, 9382 (9\/10\/9382), we can celebrate Electron Mass, or m_e Day\r\nOn Oct 09, 9382 (9\/10\/9382), we can celebrate Electron Mass, or m_e Day\r\nOn Mar 05, 9648 (9648\/5\/3), we can celebrate Faraday Constant, or F Day\r\nOn May 03, 9648 (9648\/5\/3), we can celebrate Faraday Constant, or F Day\r\nOn Feb 09, 9792 (2\/9\/9792), we can celebrate Speed of Light, or c Day\r\nOn Sep 02, 9792 (2\/9\/9792), we can celebrate Speed of Light, or c Day\r\nOn May 06, 9806 (9806\/6\/5), we can celebrate Standard Gravity, or g Day\r\nOn Jun 05, 9806 (9806\/6\/5), we can celebrate Standard Gravity, or g Day\r\n<\/pre><h4>Now it's your turn<a name=\"cbd3d377-62a1-46db-b057-0eb82070d055\"><\/a><\/h4><p>What other special numbers would you like to hold holidays for?  Measurements of the Earth?  Unit conversion factors? Interplanetary distances?  The Fibonacci sequence?  Try my function with some of your favorites and post them <a href=\"https:\/\/blogs.mathworks.com\/loren\/?p=1150#respond\">in the comments<\/a>.<\/p><script language=\"JavaScript\"> <!-- \r\n    function grabCode_7bd19516b43140c99d3163b5dde407c6() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='7bd19516b43140c99d3163b5dde407c6 ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' 7bd19516b43140c99d3163b5dde407c6';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2015 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_7bd19516b43140c99d3163b5dde407c6()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; R2015a<br><\/p><\/div><!--\r\n7bd19516b43140c99d3163b5dde407c6 ##### SOURCE BEGIN #####\r\n%% The Ultimate Pi Day is Over\u00e2\u20ac\u00a6 Now What?\r\n% Today's post is from guest blogger Dan Seal who works in the MATLAB\r\n% Product Marketing team here at MathWorks.  Dan recently celebrated Pi Day\r\n% on 3\/14\/15 and wanted to know what other holidays he might be able to\r\n% celebrate in the future.\r\n\r\n%%\r\n% Every year, mathematicians and their geeky cohort celebrate\r\n% <http:\/\/en.wikipedia.org\/wiki\/Pi_Day Pi Day> on the fourteenth of March,\r\n% a date whose written representation (3\/14) looks like the first three\r\n% digits of the mathematical constant pi (3.14).  But this year\u00e2\u20ac\u2122s Pi Day\r\n% was extra special and generated additional buzz because when you include\r\n% the year in the written date of 3\/14\/15, it gives us two more digits of\r\n% everyone\u00e2\u20ac\u2122s favorite irrational number.  And if you were like me, you may\r\n% have even marked the minute when it was 3\/14\/15 9:26, both in the AM and\r\n% again in the PM.\r\n%\r\n% But the opportunity to observe these additional digits of Pi on the\r\n% calendar is something that comes around only once per century, so I don\u00e2\u20ac\u2122t\r\n% expect to see it again.  This got me wondering if there are any other\r\n% special dates I might be able to look forward to.  M\/DD\/YY is not the\r\n% only representation of a date, and Pi is not the only special constant\r\n% out there with multiple digits.  So I collected all my favorite\r\n% mathematical and physical constants along with a slew of possible date\r\n% representations, and threw them all into MATLAB to see what it would give\r\n% me.\r\n\r\n%% Starting small\r\n% I decided to start out with just two constants which I could use to test\r\n% my work as I went along.  I selected Pi and the square root of 2.\r\n% Fortunately, MATLAB can calculate a very accurate approximation of these\r\n% values, so I didn\u00e2\u20ac\u2122t have to look up the digits.\r\nnames = {\r\n    'Archimedes'' Constant, or Pi'\r\n    'Pythagoras'' Constant, or Root 2'\r\n    };\r\nnumbers = [\r\n    pi\r\n    sqrt(2)\r\n    ];\r\n\r\n%% Defining the possible date formats\r\n% Next, I wanted to construct all the allowable date formats.  I wanted to\r\n% consider only dates that included the month, day, and year.  However, I\r\n% figure it could be a 2- or 4-digit year.  Similarly, I allowed the month\r\n% and day to each be 1 or 2 digits.  And finally, I allowed the month, day,\r\n% and year to be ordered in any of four different arrangements:\r\n%\r\n% # the American version of month\/day\/year,\r\n% # the common standard outside the US, day\/month\/year,\r\n% # the common year-first version, useful for sorting, year\/month\/day,\r\n% # and for good measure, the alternate year-first arrangement, year\/day\/month.\r\n%\r\n% MATLAB uses the <https:\/\/www.mathworks.com\/help\/matlab\/ref\/datetime.html\r\n% datetime> data type, introduced in R2014b to easily manipulate and format\r\n% dates and times.  Based on my formatting requirements above, I was able\r\n% to build all the possible datetime format strings that would meet my\r\n% criteria.\r\nyearFormats  = {'yy' 'yyyy'}; % 2 or 4 digit year\r\nmonthFormats = {'M'  'MM'  }; % 1 or 2 digit month\r\ndayFormats   = {'d'  'dd'  }; % 1 or 2 digit day\r\n\r\navailableFormats{length(yearFormats)*length(monthFormats)*length(dayFormats)*4} = '';\r\nc = 1;\r\nfor y = yearFormats\r\n    for m = monthFormats\r\n        for d = dayFormats\r\n            availableFormats{c  } = [d{:} '\/' m{:} '\/' y{:}];\r\n            availableFormats{c+1} = [m{:} '\/' d{:} '\/' y{:}];\r\n            availableFormats{c+2} = [y{:} '\/' m{:} '\/' d{:}];\r\n            availableFormats{c+3} = [y{:} '\/' d{:} '\/' m{:}];\r\n            c = c + 4;\r\n        end\r\n    end\r\nend\r\n\r\ndisp(availableFormats')\r\n\r\n%% Extracting the digits\r\n% The next task was to extract the digits from my numbers.  I figured I\u00e2\u20ac\u2122d\r\n% be using some quantities with large positive or negative exponents, so my\r\n% technique had to be robust to different types of numbers.  I decided the\r\n% best approach was to convert the numbers to strings using a consistent\r\n% format so I could easily remove any decimal points and exponential terms.\r\n% I found that |sprintf| with an exponential format could achieve this.\r\n% Keeping nine digits after the decimal point ensured that I had enough\r\n% precision to build even my longest date (which required 8 digits).  The\r\n% |char| and |arrayfun| commands allowed me to run |sprintf| on each number\r\n% individually and then build it into a character array.\r\ndigitsStr = char(arrayfun(@(x)sprintf('%1.9e',x),numbers,'UniformOutput',false));\r\n\r\ndisp(digitsStr)\r\n\r\n%%\r\n% Next, I removed the decimal point and keep only the first eight digits,\r\n% which is the most I will need.\r\ndigitsStr = digitsStr(:,[1 3:9]);\r\n\r\ndisp(digitsStr)\r\n\r\n%% Building the list of special dates\r\n% Finally, I built a loop to test each of my mathematical constants against\r\n% all the possible date formats and see which ones could be constructed as\r\n% real dates.  I tried out each possible date format using a |try\/catch|\r\n% statement.  If the date I tried to construct wasn\u00e2\u20ac\u2122t a real date, I would\r\n% catch that particular error.  But if it was, it would be added to the\r\n% list of special holidays to celebrate and the name of that constant would\r\n% be recorded as well.  I also specified a pivot year to define which\r\n% century two-digit years belong to.  Since I\u00e2\u20ac\u2122m looking or future holidays,\r\n% I decided that all two-digit years should represent dates sometime after\r\n% 2015.\r\n\r\n% Initialize arrays\r\nmaxPossibleDates = length(numbers)*length(availableFormats);\r\nholidayDates(maxPossibleDates) = datetime;\r\nholidayDates.Format = 'MMM dd, yyyy';\r\nholidayFormats{maxPossibleDates} = '';\r\nholidayNames{maxPossibleDates} = '';\r\n% Initialize counter\r\nc = 1;\r\nfor ii = 1:length(numbers) %Consider each number\r\n    for jj = 1:length(availableFormats) %For each number, consider each format\r\n        fmt = availableFormats{jj};\r\n        testFmt = strrep(fmt,'\/','');\r\n        strLength = length(testFmt);\r\n        testStr = digitsStr(ii,1:strLength);\r\n        try %If format is valid, add it to the list\r\n            holidayDates(c) = datetime(testStr,'InputFormat',testFmt,'PivotYear',2015);\r\n            holidayFormats{c} = fmt;\r\n            holidayNames{c} = names{ii};\r\n            c = c + 1;\r\n        catch err %If format errors, make sure it is the expected error\r\n            if ~strcmp(err.identifier,'MATLAB:datetime:ParseErr')\r\n                rethrow(err)\r\n            end\r\n        end\r\n    end\r\nend\r\n% Trim empty values from end of lists\r\nholidayDates = holidayDates(1:c-1);\r\nholidayFormats = holidayFormats(1:c-1);\r\nholidayNames = holidayNames(1:c-1);\r\n\r\n%%%\r\n% Because my dates are represented as datetimes, I can easily put them in\r\n% chronological order with the |sort| function.\r\n[holidayDates,ind] = sort(holidayDates);\r\nholidayFormats = holidayFormats(ind);\r\nholidayNames = holidayNames(ind);\r\n\r\n%% Printing out the results\r\n% Let\u00e2\u20ac\u2122s see how many opportunities there are to celebrate Pi Day or Root 2\r\n% Day.\r\nfor ii = 1:c-1\r\n    specialDate = holidayDates(ii);\r\n    specialDate.Format = holidayFormats{ii};\r\n    fprintf('On %s (%s), we can celebrate %s Day\\n',...\r\n        char(holidayDates(ii)),char(specialDate),holidayNames{ii})\r\nend\r\n\r\n%%%\r\n% It looks like there are a few Pi Days we can celebrate over the next 30\r\n% years.  And then there are some Root 2 Days to celebrate after that.\r\n\r\n%% Generalizing to a larger set of inputs\r\n% Since this gave me good results, I could put the entire analysis into a\r\n% function and then call it with a much longer list of my favorite\r\n% <http:\/\/en.wikipedia.org\/wiki\/Mathematical_constant mathematical> and\r\n% <http:\/\/en.wikipedia.org\/wiki\/Physical_constant physical> constants.\r\n% What are the next holidays coming up?  Be sure to mark your calendar.\r\nnames = {\r\n    'Archimedes'' Constant, or Pi'\r\n    'Euler''s Number, or e'\r\n    'Pythagoras'' Constant, or Root 2'\r\n    'Golden Ratio, or Phi'\r\n    'Root 3'\r\n    'Root 5'\r\n    'Speed of Light, or c'\r\n    'Avogadro''s Number, or N_A'\r\n    'Standard Gravity, or g'\r\n    'Gravitational Constant, or G'\r\n    'Planck Constant, or h'\r\n    'Ideal Gas Constant, or R'\r\n    'Coulomb''s Constant, or k_e'\r\n    'Elementary Charge, or e'\r\n    'Bohr Radius, or a_0'\r\n    'Electron Mass, or m_e'\r\n    'Proton Mass, or m_p'\r\n    'Atomic Mass Constant, or m_u'\r\n    'Boltzmann Constant, or k_B'\r\n    'Faraday Constant, or F'\r\n    'Stefan-Boltzmann Constant, or Theta'\r\n    'Standard Atmosphere, or atm'\r\n    'Planck Length, or l_P'\r\n    'Planck Mass, or m_P'\r\n    'Planck Time, or t_P'\r\n    'Planck Charge, or q_P'\r\n    'Planck Temperature, or T_P'\r\n    };\r\nnumbers = [\r\n    pi\r\n    exp(1)\r\n    sqrt(2)\r\n    (1+sqrt(5))\/2\r\n    sqrt(3)\r\n    sqrt(5)\r\n    299792458\r\n    6.02214129e23\r\n    9.80665\r\n    6.67384e-11\r\n    6.62606957e-34\r\n    8.3144621\r\n    8.9875517873681764e9\r\n    1.602176565e-19\r\n    5.2917721092e-11\r\n    9.10938291e-31\r\n    1.672621777e-27\r\n    1.660538921e-27\r\n    1.3806488e-23\r\n    96485.3365\r\n    5.670373e-8\r\n    101325\r\n    1.616199e-35\r\n    2.17651e-8\r\n    5.39106e-44\r\n    1.875545956e-18\r\n    1.416833e32\r\n    ];\r\n\r\nholidayForFamousConstants(numbers,names)\r\n\r\n%% Now it's your turn\r\n% What other special numbers would you like to hold\r\n% holidays for?  Measurements of the Earth?  Unit conversion factors?\r\n% Interplanetary distances?  The Fibonacci sequence?  Try my function with\r\n% some of your favorites and post them\r\n% <https:\/\/blogs.mathworks.com\/loren\/?p=1150#respond in the comments>.\r\n##### SOURCE END ##### 7bd19516b43140c99d3163b5dde407c6\r\n-->","protected":false},"excerpt":{"rendered":"<!--introduction--><p>Today's post is from guest blogger Dan Seal who works in the MATLAB Product Marketing team here at MathWorks.  Dan recently celebrated Pi Day on 3\/14\/15 and wanted to know what other holidays he might be able to celebrate in the future.... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/loren\/2015\/03\/16\/the-ultimate-pi-day-is-over-now-what\/\">read more >><\/a><\/p>","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[57,33],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/posts\/1150"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/comments?post=1150"}],"version-history":[{"count":4,"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/posts\/1150\/revisions"}],"predecessor-version":[{"id":1155,"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/posts\/1150\/revisions\/1155"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/media?parent=1150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/categories?post=1150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/loren\/wp-json\/wp\/v2\/tags?post=1150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}