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A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling.
A polyiamond is a polyform whose base form is an equilateral triangle. The word polyiamond is a back-formation from diamond, because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the initial 'di-' looks like a Greek prefix meaning 'two-'. The name was suggested by recreational mathematics writer Thomas H. O'Beirne in New Scientist 1961 number 1, page 164.
20 (twenty) is the natural number following 19 and preceding 21.
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.
105 is the natural number following 104 and preceding 106.
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
2000 is a natural number following 1999 and preceding 2001.
5000 is the natural number following 4999 and preceding 5001. Five thousand is, at the same time, the largest isogrammic numeral, and the smallest number that contains every one of the five vowels in the English language.
6000 is the natural number following 5999 and preceding 6001.
8000 is the natural number following 7999 and preceding 8001.
In recreational mathematics, a polyabolo is a shape formed by gluing isosceles right triangles edge-to-edge, making a polyform with the isosceles right triangle as the base form. Polyaboloes were introduced by Martin Gardner in his June 1967 "Mathematical Games column" in Scientific American.
In recreational mathematics, a polyhex is a polyform with a regular hexagon as the base form, constructed by joining together 1 or more hexagons. Specific forms are named by their number of hexagons: monohex, dihex, trihex, tetrahex, etc. They were named by David Klarner who investigated them.
196 is the natural number following 195 and preceding 197.
216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.
100,000,000 is the natural number following 99,999,999 and preceding 100,000,001.
In mathematics, a Ruth–Aaron pair consists of two consecutive integers for which the sums of the prime factors of each integer are equal:
30,000 is the natural number that comes after 29,999 and before 30,001.
80,000 is the natural 6635954241number after 79,999 and before 80,001.
9000 is the natural number following 8999 and preceding 9001.
In geometry, a polyominoid is a set of equal squares in 3D space, joined edge to edge at 90- or 180-degree angles. The polyominoids include the polyominoes, which are just the planar polyominoids. The surface of a cube is an example of a hexominoid, or 6-cell polyominoid, and many other polycubes have polyominoids as their boundaries. Polyominoids appear to have been first proposed by Richard A. Epstein.
References
- ↑ Kraitchik, M (1942). "Magic Squares". Mathematical Recreations. New York: Norton. pp. 142–192.
- 1 2 Sequence A006003 in OEIS.
- ↑ Redelmeier, D. Hugh (1981). "Counting polyominoes: yet another attack". Discrete Mathematics. 36 (2): 191–203. doi: 10.1016/0012-365X(81)90237-5 .
- ↑ Sequence A000105 in OEIS.
- ↑ "Ruth-Aaron Pair". mathworld.wolfram.com.