FIGURATE NUMBERS

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FIGURATE NUMBERS

• By Amber Y.
• Precal 5th Hour

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What is a Figurate Number????

• Figurate numbers are sequences generated by
  figures made up of evenly spaced dots.
• Figurate numbers include the triangular numbers,
  square numbers, pentagonal numbers, etc.
  Sometimes they are called polygonal numbers if
  they form regular polygons.

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Some Types of Figurate Numbers

• Triangle
• Square
• Polygonal
• Hexagonal
• Pentagonal

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Triangular Figurate Numbers

• It can be represented in the form of a triangular
  grid of points where the first row contains a
  single element and each row to follow contains
  one more element than the previous one.

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Square Figurate Numbers
A square number, also called a perfect square, is
a figurate number of the form , where n is an
integer. For example the square numbers for , 1,
... are 0, 1, 4, 9, 16, 25, 36, 49, ...
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Polygonal, Hexagonal, and Pentagonal
Polygonal is a generalization of triangular,
square,etc., figurate numbers
A polygonal number and it goes in the form of 6.
The first few are 1, 6, 15, 28, 45, ...
A polygonal number that goes in the forms of 5.
1, 5, 12, 22
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Who Invented Figurate Numbers?

• The Pythagoreans invented Figurate Numbers in the
  18th century.
• This type of number was also called looping.

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The End