Easter algorithm chapter (#673)

* adding rough draft of intro to computus chapter * adding rough draft of chapter, need to add visuals and code * k-q has been changed to correctly reflect the fact that it is non-observed leapdays * adding correction to p term * fixing text and adding source code * adding computus chapter with gauss's Easter algorithm * Adding new visualization and fixing grammar Co-authored-by: lockcmpxchg8beax

Author: leios

SUMMARY.md

@@ -35,3 +35,4 @@
 *[Data Compression](contents/data_compression/data_compression.md)
 *[Huffman Encoding](contents/huffman_encoding/huffman_encoding.md)
 *[Quantum Information](contents/quantum_information/quantum_information.md)
+*[Computus](contents/computus/computus.md)

contents/computus/code/julia/gauss_easter.jl

@@ -0,0 +1,63 @@
+functioncomputus(year; servois=false)
+
+# Year's position on the 19 year metonic cycle
+ a =mod(year, 19)
+
+# Century index
+ k =floor(Int, year/100)
+
+# Shift of metonic cycle, add a day offset every 300 years
+ p =floor(Int, (13+8* k) /25) 
+
+# Correction for non-observed leap days
+ q =floor(Int, k /4)
+
+# Correction to starting point of calculation each century
+ M =mod(15- p + k - q, 30)
+
+# Number of days from March 21st until the full moon
+ d =mod(19* a + M, 30)
+
+# Returning if user wants value for Servois' table
+if servois
+returnmod(21+d,31)
+end
+
+# Finding the next Sunday
+# Century-based offset in weekly calculation
+ N =mod(4+ k - q, 7)
+
+# Correction for leap days
+ b =mod(year, 4)
+ c =mod(year, 7)
+
+# Days from d to next Sunday
+ e =mod(2* b +4* c +6* d + N, 7)
+
+# Historical corrections for April 26 and 25
+if (d ==29&& e ==6) || (d ==28&& e ==6&& a >10)
+ e =-1
+end
+
+# Determination of the correct month for Easter
+if(22+ d + e >31)
+return"April "*string(d + e -9)
+else
+return"March "*string(22+d+e)
+end
+end
+
+# Here, we will output the date of the Paschal full moon
+# (using Servois notation), and Easter for 2020-2030
+
+a = [i for i =2020:2030]
+servois_numbers =computus.(a;servois=true)
+easter_dates =computus.(a)
+
+println("The following are the dates of the Paschal full moon (using Servois "*
+"notation) and the date of Easter for 2020-2030 AD:")
+println("Year Servois number Easter")
+for i =1:length(a)
+println(string(a[i])*"\t"*string(servois_numbers[i])*"\t\t"*
+string(easter_dates[i]))
+end

contents/computus/computus.md

@@ -1,3 +1,7 @@
+#------------------------------------------------------------------------------#
+# FFT
+#------------------------------------------------------------------------------#
+
 @article{ct1965,
 title={An algorithm for the machine calculation of complex Fourier series},
 author={Cooley, James W and Tukey, John W},
@@ -9,6 +13,10 @@ @article{ct1965
 publisher={JSTOR}
 }
 
+#------------------------------------------------------------------------------#
+# Convex Hull
+#------------------------------------------------------------------------------#
+
 @article{jm1973,
 title={On the identification of the convex hull of a finite set of points in the plane},
 author={Jarvis, Ray A},
@@ -31,8 +39,74 @@ @article{gs1972
 publisher={Elsevier}
 }
 
+#------------------------------------------------------------------------------#
+# Plotting
+#------------------------------------------------------------------------------#
+
 @misc{gnuplot,
 title={Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation},
 author={Williams, T and Kelley, C},
 year={2015}
 }
+
+#------------------------------------------------------------------------------#
+# Computus
+#------------------------------------------------------------------------------#
+
+@book{bede725,
+title={Bede, the Reckoning of Time},
+author={Venerabilis, Beda and others},
+volume={29},
+year={1999},
+publisher={Liverpool University Press}
+}
+
+@misc{dictcomputus,
+title={Dictionary.com definition of computus},
+url={https://www.merriam-webster.com/dictionary/computus},
+year={2020}
+}
+
+@article{computus1876,
+title={To find Easter: a new York correspondent sends us the following},
+author={unknown},
+journal={Nature},
+year={1876}
+}
+
+@article{bien2004,
+title={Gauss and beyond: The making of Easter algorithms},
+author={Bien, Reinhold},
+journal={Archive for history of exact sciences},
+volume={58},
+number={5},
+pages={439--452},
+year={2004},
+publisher={Springer}
+}
+
+@inproceedings{servois,
+title={84 Calendrier},
+author={Servois, M},
+booktitle={Annales de Mathématiques pures et appliquées},
+volume={4},
+number={1813-1814},
+pages={84--90}
+}
+
+@article{standish2004,
+title={The astronomical unit now},
+author={Standish, EM},
+journal={Proceedings of the International Astronomical Union},
+volume={2004},
+number={IAUC196},
+pages={163--179},
+year={2004},
+publisher={Cambridge University Press}
+}
+
+@misc{lunar_month_wiki,
+title={Wikipedia: Lunar Month},
+url={https://en.wikipedia.org/wiki/Lunar_month},
+year={2020}
+}