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In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.
The first known trigonometric table, compiled by Hipparchus in the 2nd century BC, is no longer extant but tabulated the value of the chord function for every 7 + 1 / 2 degrees. In the 2nd century AD, Ptolemy compiled a more extensive table of chords in his book on astronomy , giving the value of the chord for angles ranging from 1 / ...
In India and Tibet, three four-sided long dice were rolled sequentially as an oracle, to produce 1 of 64 possible outcomes. [ 4 ] The ancient Mesopotamian Royal Game of Ur uses eight four-sided pyramid-shaped dice made out of rock, half of them colored white, and half black.
By Cauchy–Schwarz inequality, the argument of the arccosine is in the interval [−1, 1]. Therefore θ is real, and 0 ≤ θ ≤ π (or 0 ≤ θ ≤ 180 if angles are measured in degrees). Angles are not useful in a Euclidean line, as they can be only 0 or π. In an oriented Euclidean plane, one can define the oriented angle of two vectors.
Every prime number p divides a Fibonacci number that can be determined by the value of p modulo 5. If p is congruent to 1 or 4 modulo 5, then p divides F p−1, and if p is congruent to 2 or 3 modulo 5, then, p divides F p+1. The remaining case is that p = 5, and in this case p divides F p.
[3] [5] A little earlier than Kepler, Pedro Nunes wrote about it in 1567, and it is "likely to have been widespread in late medieval and Renaissance manuscript traditions". [3] It has also been independently rediscovered several times, later than Kepler. [1] A right triangle formed by an edge midpoint, base center point, and apex of a square ...
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
It was discovered by Charles Messier on June 5, 1764. [4] Its name means 'three-lobe'. The object is an unusual combination of an open cluster of stars , an emission nebula (the relatively dense, reddish-pink portion), a reflection nebula (the mainly NNE blue portion), and a dark nebula (the apparent 'gaps' in the former that cause the ...