Teaching Kids Programming – Pythagorean Theorem and Algorithm to Find Pythagorean Numbers

Teaching Kids Programming: Videos on Data Structures and Algorithms

Proof-Pythagorean-Theorem

Proof of Pythagorean Theorem

The big square’s area is and it is equal to 4 triangls + a small square.

therefore:

Bruteforce Algorithm to Find Pythagorean Numbers

Given c – a integer, let’s find all distinct positive pairs (a smaller or equal than b and

Then, we can iterate a from 1 till b is smaller than a. We can compute the value of when a is fixed. Then, we just need to check if b is a perfect square – this can be done using inbuilt sqrt function or binary search algorithm.

from math import sqrt

def f(c):
    a = 1
    while c * c >= 2 * a * a:
        b2 = c * c - a * a
        b = int(sqrt(b2))
        if b * b == b2:
            print("(%d)^2 + (%d)^2 = (%d)^2" % (a, b, c))
        a += 1

f(5)
f(10)
f(50)
f(100)

Output:

(3)^2 + (4)^2 = (5)^2
(6)^2 + (8)^2 = (10)^2
(14)^2 + (48)^2 = (50)^2
(30)^2 + (40)^2 = (50)^2
(28)^2 + (96)^2 = (100)^2
(60)^2 + (80)^2 = (100)^2

Finding Pythagorean Triplets in an Array – we can use Two Pointer Algorithm or Bruteforce with Hash Set: Teaching Kids Programming – Finding Pythagorean Triplets in Array using Two Pointer or Hash Set

–EOF (The Ultimate Computing & Technology Blog) —