什麼是四角形數?求求大家幫忙解釋一下?

2015-12-14 2:22 pm

回答 (1)

2015-12-14 8:17 pm
It's not clear if the following answer is what you need, but I will explain what a "cyclic quadrilateral number" is anyway.

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex.

A "cyclic quadrilateral number" n is an integer with decomposition into integers a, b, c, d such that the area of the quadrilateral with sides a, b, c, d is an integer, and the circumradius R is also an integer.

An example is 2304=8*8*6*6. The cyclic quadrilateral (rhombus) can be decomposed into two congruent right triangles with legs 6 and 8, hence the area is 48 (integer). The circumradius is half of the hypotenuse of the right triangles and equals 5, another integer.

Another example is 2822400=24*24*70*70, or 2822400=40*40*42*42.
參考: OEIS: https://oeis.org/A218431


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