Date as Pythagorean triples

[Tigers!]

24th July 2025 (07/24/25) is a Pythagorean triple.

I obviously have too much spare time on my hands.

 

[James Brown]

We better enjoy these while they last. According to a reddit post, the next PT date will be 2026-10-24.

After that? April 5th, 2103.

 

[Spacetime Inhabitant]

Isn't it cheating to only use the 25 and 26 parts of 2025 and 2026?
April 5th = 4^2 + 5^2 = 16 + 25 = 41. How does that relate to 2103?

 

[bilby]

Isn't it cheating to only use the 25 and 26 parts of 2025 and 2026?
April 5th = 4^2 + 5^2 = 16 + 25 = 41. How does that relate to 2103?

It relates to 27 May, in the year 6 (BCE or CE, makes no difference*).

SQRT(41) = 6.403; May 27 is 0.403 of the way through the year. So the relevant date is the fifth of April, of the year approximately May the twenty seventh, six CE.

Probably.

The high-pitched whine emanating from the south of Italy is Pythagoras spinning in his grave...










* As any fool knows, everything that happened in the past, happened at the same time.

 

[Swammerdami]

(12709, 13500, 18541) is a Pythagorean triple "published" in Babylon more than 1000 years before Pythagoras was even born! Does this seem remarkable? I think this triple is the 4th line (after the "heading") in this photo of the ancient clay tablet:

[Item 322 in the Plimpton collection of cuneiform tablets in the Colombia University] listed fifteen Pythagorean triples. Lest you entertain for even a split second the idle thought that people couldn’t have known such advanced mathematics thirty-eight centuries ago and that these triples were probably hit upon by trial and error, let it be noted that the largest triple (in Plimpton 322) is {12709, 13500, 18541}. More amazingly, these were the work of a pupil probably doing his assigned homework from school.

I've had an off-and-on interest in Pythagorean triples. Note that matrices like

( 17 0 0 // 0 8 15 // 0 15 - 8 ) ÷ 17​

are orthogonal and useful in high-speed signal processing. Multiplication by such matrices is achieved with integer arithmetic.

 

[Swammerdami]

I found Plimpton 322 interesting enough to pursue a bit further.

this webpage explains that the tablet is a table of (rational-valued) sines in order! It explains that the fourth line, reproduced below, should consist of the Babylonian numerals

1.53.10.29.32.52.16 // 3.31.49 // 5.09.01 // ki 4​

The 2nd and 3rd numbers here are indeed the sides of the pythagorean triangle

12709 = 3*3600 + 31*60 + 49 // written 3 3 1 4 9 in the (3600,600,60,10,1) Babylonian base.​

13500 = 3*3600 + 45*60 + 0 // written 3 4 5 0 0 (or just 3 4 5) in Babylonian base (with space used for zero)​

18541 = 5*3600 + 9*60 + 1 // written 5 0 9 0 1 (or just 5 9 1)​

Confirm that these numbers satisfy the Pythagorean identity by typing the following into Google and seeing the result '0.'

(3*3600 + 31*60 + 49)^2 + (3*3600 + 45*60 + 0)^2 - (5*3600 + 9*60 + 1)^2​

It's hard to read the Babylonian numerals, but I show, with red ink I've added that it APPEARS to follow the pattern shown at above webpage:

1.53.10.29.32.52.16 // 3.31.49 // 5.09.01 // ki 4​

though the initial '1.53.10' and final 'ki 4' are missing from the clay fragment.

 

[Bomb#20]

Isn't it cheating to only use the 25 and 26 parts of 2025 and 2026?
April 5th = 4^2 + 5^2 = 16 + 25 = 41. How does that relate to 2103?

03^2 + 4^2 = 5^2. The year was the hypotenuse in the first two examples, but that wasn't a requirement, just chance.

If you want to use all parts of the year, we could do January 5, 2025.

 

[lpetrich]

Pythagorean triple - Wikipedia

Positive integers \( \{ a, b, c \} \) satisfying: \( a^2 + b^2 = c^2 \)

A primitive one is where a, b, and c are all coprime (relatively prime). Every general one is some positive integer k times some primitive one: \( \{k a, k b, k c\} \)

Euclid's formula, for m, n: \( a = m^2 - n^2 ,\ b = 2 m n ,\ c = m^2 + n^2 \)

Primitive if and only if (iff, two f's) m and n are coprime and one and only one of them is even. This formula generates every primitive triple, and by relaxing these constraints on m and n, one gets many non-primitive ones, though not all of them.

There are several other methods, described in Formulas for generating Pythagorean triples - Wikipedia