ECOLE MONDIALE WORLD SCHOOL MUMBAI

GRADE 8 INVESTIGATING PATERNS TASK CRITERIA B,C & D

Finding Primitive Pythagorean Triples

Three ascending whole numbers form a Pythagorean triple when the square of the first number added to the square of the second number is equal to the square of the third number. Here are four Primitive Pythagorean Triples (the three integers have greatest common divisor equal to 1. and all other Pythagorean Triples are multiples of Primitive Pythagorean Triples).

First345Second51213Third72425Fourth94041

1. Study the pattern found in these numbers and then write down four more Primitive Pythagorean Triples

(i)the numbers in the fifth triple

(ii)the numbers in the sixth triple

(iii)the numbers in the seventh triple

(iv)the numbers in the eight triple

2. Write the general rule that you have found to write primitive Pythagorean triples. For each of those sets of numbers use your calculator to verify that the square of the largest is equal to the sum of the squares of the other two numbers.

3. Study your eight Primitive Pythagorean Triples and see if you can discover any other interesting sequences that exist between the numbers.

After completing all this work you can claim to be a member of the famous secret society called the Pythagoreans whose members founded a school of mathematics and philosophy at Crotona in southern Italy around the year 540 BC.