| 词条 | Magic triangle (mathematics) |
| 释义 |
A magic triangle (also called a perimeter magic triangle[1]) is an arrangement of the integers from 1 to {{mvar|n}} on the sides of a triangle with the same number of integers on each side, called the order of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle.[1][2][3][4] Unlike magic squares, there are different magic sums for magic triangles of the same order.[1] Any magic triangle has a complementary triangle obtained by replacing each integer {{mvar|x}} in the triangle with {{math|1 + n − x}}. This means that only half of the triangles for any order need to be checked for the magic property.[1] ExamplesOrder-3 magic triangles are the simplest (except for trivial magic triangles of order 1).[1] See also{{Div col|cols=|content=
References1. ^1 2 3 4 {{Cite web|url=http://www.magic-squares.net/perimeter.htm|title=Perimeter Magic Triangles|website=www.magic-squares.net|access-date=2016-12-27}} {{Magic polygons}}2. ^{{Cite web|url=http://www.trottermath.net/simpleops/pmp.html|title=Perimeter Maghic Polygons|website=www.trottermath.net|access-date=2016-12-27}} 3. ^{{Cite web|url=http://nrich.maths.org/1983|title=Magic Triangle : nrich.maths.org|website=nrich.maths.org|access-date=2016-12-27}} 4. ^{{Cite web|url=http://cemc.uwaterloo.ca/resources/p4w/archive/p4w8_magic_triangles_and_other_figures.pdf|title=P4W8: Magic Triangles and Other Figures|last=|first=|date=|website=|publisher=|access-date=December 27, 2016}} 1 : Magic squares |
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