带整中位数的整边三角形
Integer-Sided Triangles with integral medians
摘要：
本文证明了三条边长为整数的三角形的三条中线不可能都为整数长，这在命题2中已作了证明。在第五节中，我们给出了精确的（即必要和充分）条件的非等腰，整数边三角形有两个整数中位数。在第3节，我们给出了三类特殊的整数边三角形的参数描述。2第一类三角形由所有的勾股三角形组成，它们的中线是整数。任何毕达哥拉斯三角形的另外两个中线（两条边的中线）都是无理数，这一事实的证明可以在文献4中找到。第二族由所有整数边的等腰三角形组成，其唯一的整数中线是包含在等长两边之间的中线。最后，第三族由所有等腰整数边三角形组成，两个中线长度相等;具有整数长度。
英文摘要：
In this work, we prove that any triangle whose three sidelengths are integers, cannot have all of its three medians also having integral lengths.This is done in Proposition 2.In Section 5, we give precise(i.e.necessary and sufficient)conditions for a nonisosceles, integer-sided triangle to have two integral medians.In Section 3, we offer parametric descriptions of three special families of integer-sided triangles.The first family consists of all Pythagorean triangles whose medians to their hypotenuses is integral. The other two medians (to the two legs)of any Pythagorean triangle are irrational, a proof of this fact can be found in reference 4 of this paper.The second family consists of all integer-sided isosceles triangles, whose only integral median is the one contained between the two sides of equal length. Finally, the third family consists of all isosceles integer-sided triangles with the two medians of equal length;having integer length.
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