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The most surprising of these is that the sum of the numbers in the triangles that point upwards is the same as the sum of those in triangles that point downwards (no matter how large the T-hexagon). In the above example, 17 + 20 + 22 + 21 + 2 + 6 + 10 + 14 + 3 + 16 + 12 + 7 = 5 + 11 + 19 + 9 + 8 + 13 + 4 + 1 + 24 + 15 + 23 + 18 = 150
Centered hexagonal numbers appearing in the Catan board game: 19 land tiles, 37 total tiles. In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, [1] [2] is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice.
L14 Sinus Iridum. The Lunar 100 (L100) is a list of one hundred of the most interesting features to observe on the Moon.The list was first described by Charles A. Wood in the article The Lunar 100 in Sky & Telescope magazine, April 2004.
As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction 5 / 7 when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...
In 1736, Leonhard Euler published a proof of Fermat's little theorem [1] (stated by Fermat without proof), which is the restriction of Euler's theorem to the case where n is a prime number. Subsequently, Euler presented other proofs of the theorem, culminating with his paper of 1763, in which he proved a generalization to the case where n is ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
7 Other named large numbers used in mathematics, ... 1 10 9: Billion Thousand million Milliard G Giga-3 2 ... (This is the value of n when 10,000 × 10 6n = 10 10 100
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: