Geometry: An Interactive Journey to Mastery

The Geometry of Figurate Numbers

Lesson 34

Topics
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x Square, triangular, and squangular numbers.
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x squangular number: A number that is both square and triangular.
x square number: A number is a square number if a count of that many pebbles can be arranged in a
square array.
x triangular number: A number is a triangular number if a count of that many pebbles can be arranged
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Formulas
x 123    "" NNN 1 1 321 N^2.
x 7KHVXPRIWKH¿UVWN odd numbers is N^2.
x 7KHVXPRIWKH¿UVWN even numbers is Nͼ௘N௘ͽ
x 7KHVXPRIWKH¿UVWN counting numbers is 123   " N NN^2 ^1.
x The Nth square number is Sͼ௘1࣠ͽ = N^2.
x The Nth triangular number is TN NN^2 ^1.
Summary
The Greeks of antiquity saw all of mathematics though the lens of geometry—even number theory. In this
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geometric arrangements, sophisticated summation formulas.