Linear number
In mathematics, a linear number is a figurate number that follows a pattern where the nth linear number ln is equal to the nth whole number, or natural number.[1][2] A linear number is the simplest form of a figurate number. The triangular numbers can be found by adding up sequential linear numbers, that is, a linear number is a gnomon for the triangular numbers.[3] Such gnomons played a role in the mathematical investigations of Pythagoras.[4]
The first 100 linear numbers are as follows:
1, 2, 3 ... 97, 98, 99, 100
The nth linear number can be derived using this formula:
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References[edit]
- ↑ Deza, Elena; Deza, Michel Marie. Figurate Numbers. World Scientific. p. 4. ISBN 9789814458535. Search this book on
- ↑ Ferretti, Elena. The Cell Method: A Purely Algebraic Computational Method in Physics and Engineering. Momentum Press. pp. section 101-102. ISBN 9781606506066. Search this book on
- ↑ Gazalé, Midhat J. Gnomon: From Pharaohs to Fractals. Princeton University Press. p. 16. ISBN 0691005141. Search this book on
- ↑ Schaaf, Willian L. "number game". britannica.com. Encyclopedia Britannica. Retrieved 2 July 2016.
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