The old Chinese proverb, “A picture is worth a thousand words,” is true in mathematics. We frequently use geometric illustrations to clarify concepts and illustrate relationships in every branch of mathematics. Figurate Numbers provide such a link between number theory and geometry; they are positive integers that can be represented by geometric patterns. Although the Pythagoreans are usually given credit for their discovery, the ancient Chinese seem to have originated such representations about 500 years before Pythagoras. Many centuries later, in 1665, Pascal wrote a book on them, Treatise on Figurate Numbers.
KeywordsSummation Formula Triangular Array Fermat Number Recursive Definition Lucas Number
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