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Farey sunburst of order 6, with 1 interior (red) and 96 boundary (green) points giving an area of 1 + 96 / 2 − 1 = 48 [1]. In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary.
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
Other magic triangles use Triangular number or square number of vertices to form magic figure. Matthew Wright and his students in St. Olaf College developed magic triangles with square numbers. In their magic triangles, the sum of the k-th row and the (n-k+1)-th row is same for all k.
Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book Elements in 300 BCE. [1] In 499 CE Aryabhata, used this illustrated method in the Aryabhatiya (section 2.6). [2] Although simple, this formula is only useful if the height can be readily found, which is not always the case.
if the last digit of a number is 2 or 8, its square ends in an even digit followed by a 4; if the last digit of a number is 3 or 7, its square ends in an even digit followed by a 9; if the last digit of a number is 4 or 6, its square ends in an odd digit followed by a 6; and; if the last digit of a number is 5, its square ends in 25.
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. [1] [2] Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers. As an example, starting with the number 8991 in base 10: