The Pythagoreans represented whole numbers as geometric shapes, often with pebbl

Question

The Pythagoreans represented whole numbers as geometric shapes, often with pebbles on the sand. The Pythagoreans discovered many relationships between these numbers. Complete the table, and then complete the statements below based on these relationships. The sum of two consecutive triangular numbers is a(n) ___ number. Two times any triangular number is a(n) ___ number. Eight times a triangular number plus one is a(n) ___ number. Three times any triangular number plus the next triangular number is a(n) ___ number. An oblong number plus the corresponding square number is a(n) ___ number. A triangular number plus the corresponding square number minus the corresponding oblong number is a(n) ___ number.

Explanation / Answer

a) Sum of two consecutive number is a Square Number, i.e. 1+3 = 4, 3+6=9

B) Two times any triangular number is Oblong number

c) Eight times a triangular number plus one is equal to Square number

e) Odd number

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Triangular 1 3 6 10 15 21 28 36 45 55 Square 1 4 9 16 25 36 49 64 81 100 Oblong 2 6 12 20 30 42 56 72 90 110

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