A formula that describes the famous Yang Hui or Pascal's Triangle If you enlarge a square, you need two new rectangles of the same size and a square. The area of these rectangles and the square must be a square number, if you want to find the Pythgorean triples ab,c with a²+b²=c²

Visualization of the Yang Hui or Pascal's Triangle, dimensions 0, point, 1, line, 2, square, 3, cube, with LEGOs. Blue: the starting bodies white, gray, red, black: the components that are added, for example two rectangles and a square or three wall elements, three edge elements and a cube To find any Pythagorean triple 2025 belongs to, find its divisors: 2025=45²=3⁴*5² =1*2025 =3*675 =5*405 =9*225 =15*1350 =25*81 =27*75 =45*45 =75*27 =81*25 =135*15 =225*9 =405*5 =675*3 There are 14 combinations, therefore 2025 belongs to 14 Pythagorean triples. If d=1, b=2ad+d², then 2a+1= 2025 2025-1=2a, a=1012, b²=2025, c=1013: => 1012²+45²=1013² works without multiplikations! This is a primitive Pythagorean triple.

Hi fam,
have a fulfilling year 45² that equals 2025!
2025 is a square number and belongs to 14 Pythagorean triples.
(d(m²-1)/2)²+d²m²=(d(m²+1)/2)²
d=1, m=2025
2050312²+2025²=2050313²
CHEAP TRICK: ALT: 1012²+2025=1013²
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