如何在给定区域时找到三角形的所有可能边 [英] how to find all possible sides of a triangle when the area is given

问题描述

C ++

如何在给出区域时找到三角形的所有可能边

其中区域和边是自然数

C++
how to find all possible sides of a triangle when the area is given
where the area and sides are natural numbers

推荐答案

另一方面，我打赌 Heronian Triangle [ ^ ]。

On the other hand, I would bet on the Heronian Triangle[^].

这不是编程任务，而是一个几何问题。

知道所有具有给定基边和给定高度的三角形具有相同的面积，您可以为给定区域选择任意基边并进行相邻点扫描从无限左到无限右平行高度距离到baes线，始终保持相同的面积（面积的两倍=基本长度乘以高）。这为每个任意选择的基线提供了infinte数量的边。



所以，问题是，如果有进一步的限制。如果没有，你有无限多的边，更糟糕的是，即使对于有限的区域，有些两边也可能变得无限。



干杯

Andi



PS：给定区域可能没有或有很多解决整数的问题。

This is not a programming task but rather a geometrical problem.
Knowing that all triangles with a given base side and a given height have the same area, you can chose for a given area an arbitrary base side and have the adjacent point sweep from infinite left to infinite right on a parallel of height distance to the baes line, always maintaining the same area (two times the area = base length times hight). This gives infinte number of sides for each arbitrarily chosen base line.

So, the question is, if there are further constraints. If not, you have infinite number of sides and even worse, some two sides may become infinite, even for a finite area.

Cheers
Andi

PS: There may for a given area be no or many solutions for integral numbers.

我最好的选择是苍鹭公式 [ ^ ]

My best bet would be Herons Formula[^]

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