lego_triples.py

#!/usr/bin/env python3
import math

# Poor man's numpy.arange
LENGTHS = []
for i in range(1, 32):
    LENGTHS.extend([i, i+0.5])

#     |\      y - from vertex to top
#     | \     x - from vertex to right
#     |  \    u - from vertex to top of second triangle
#     |   \   v - intersection to left
#     |y   \
# --v-|     \
#  \  |      \
#   \ u       \
#    \|____x___\
#
def find_fourths(s1, s2):
    global i
    ratio = s1 / s2
    angle = math.degrees(math.atan(ratio))
    target_angle = 90 - angle
    fourths = []
    for x in LENGTHS:
        for y in LENGTHS:
            if (x != s1 and y != s2) and (x != s2 and y != s1) and is_pythagorean_triple(x, y):
                # now check the angle
                interior_angle = math.degrees(math.atan(x / y))
                diff = abs(interior_angle - target_angle)
                if diff == 0.0:
                    fourths.append((x, y, target_angle))
    return fourths


def is_pythagorean_triple(s1, s2):
    hypotenuse = math.sqrt(math.pow(s1, 2) + math.pow(s2, 2))
    diff = abs(hypotenuse - round(hypotenuse))
    return diff < 0.005


for side_1 in LENGTHS:
    for side_2 in LENGTHS:
        if is_pythagorean_triple(side_1, side_2):
            result = find_fourths(side_1, side_2)
            if len(result) > 0:
                print(f'Found {len(result)} for y: {side_1}, x: {side_2}')
                for fourth in result:
                    print(f'\tv: {fourth[0]}, u: {fourth[1]}, angle: {fourth[2]}')