| Math Logic |
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| Question : |
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What are 'Figurate Numbers' ? |
Answer : |
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A figurate number, also (but mostly in texts from the 1500 and 1600s) known as a figural number. |
| They are just
numbers or a series of numbers formed from an arithmetical progression
in which the first term is unity and the difference a whole
number, by taking the first two, first three, first four, etc.,
terms and forming a new series, and so on, by forming in the
same way. |
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The numbers of each sequence, when represented by points, can be
systematically arranged in various geometrical figures such as triangles, pentagons, tetrahedrons, etc.
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The n-th regular r-topic number is given by the formula :
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for n >= 2
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where, r! is the factorial of r, 
is a binomial coefficient, and n(r) is the rising factorial.
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For Example,
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1
3
6
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