Gauss's diary
Encyclopedia
Gauss's diary was a record of the mathematical discoveries of C. F. Gauss from 1796 to 1814. It was rediscovered in 1897 and published by , and reprinted in volume X1 of his collected works.
Entry 1, dated 1796, March 30, states "Principia quibus innititur sectio circuli, ac divisibilitus eiusdem geometrica in septemdecim partes etc.", which records Gauss's discovery of the construction of a heptadecagon
by ruler and compass.
Entry 10, dated 1796, July 10, states "ΕΥΡΗΚΑ
! num = Δ + Δ + Δ" and records his discovery of a proof that any number is the sum of 3 triangular numbers, a special case of the Fermat polygonal number theorem
.
Entry 43, dated 1796, October 21, states "Vicimus GAGAN". Its meaning is unclear.
Entry 146, dated 1814 July 9, is the last entry, and records an observation relating biquadratic residues and the leminiscate functions, later proved by Gauss and by . More precisely, Gauss observed that if a+bi is a (Gaussian) prime and a–1+bi is divisible by 2+2i, then the number of solutions to the congruence 1=xx+yy+xxyy (mod a+bi), including x=∞, y=±i and x=±i, y=∞, is (a–1)2+b2.
Sample entries
Most of the entries consist of a brief and sometimes cryptic statement of a result in Latin.Entry 1, dated 1796, March 30, states "Principia quibus innititur sectio circuli, ac divisibilitus eiusdem geometrica in septemdecim partes etc.", which records Gauss's discovery of the construction of a heptadecagon
Heptadecagon
In geometry, a heptadecagon is a seventeen-sided polygon.-Heptadecagon construction:The regular heptadecagon is a constructible polygon, as was shown by Carl Friedrich Gauss in 1796 at the age of 19....
by ruler and compass.
Entry 10, dated 1796, July 10, states "ΕΥΡΗΚΑ
Eureka (word)
"Eureka" is an interjection used to celebrate a discovery, a transliteration of a word attributed to Archimedes.-Etymology:The word comes from ancient Greek εὕρηκα heúrēka "I have found ", which is the 1st person singular perfect indicative active of the verb heuriskō "I find"...
! num = Δ + Δ + Δ" and records his discovery of a proof that any number is the sum of 3 triangular numbers, a special case of the Fermat polygonal number theorem
Fermat polygonal number theorem
In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most -gonal numbers. That is, every positive number can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of...
.
Entry 43, dated 1796, October 21, states "Vicimus GAGAN". Its meaning is unclear.
Entry 146, dated 1814 July 9, is the last entry, and records an observation relating biquadratic residues and the leminiscate functions, later proved by Gauss and by . More precisely, Gauss observed that if a+bi is a (Gaussian) prime and a–1+bi is divisible by 2+2i, then the number of solutions to the congruence 1=xx+yy+xxyy (mod a+bi), including x=∞, y=±i and x=±i, y=∞, is (a–1)2+b2.