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Little explorations with HP calculators (no Prime)
04-07-2017, 11:39 PM (This post was last modified: 04-07-2017 11:40 PM by Gerson W. Barbosa.)
Post: #151
RE: Little explorations with the HP calculators
(04-07-2017 10:19 PM)Han Wrote:  Please explain how the shape being irrelevant is clear to you. What are the logical deductive steps to conclude that the shape is irrelevant? You wrote in an earlier post that this is true if the base and height are constant. For one triangle, assume that x=y=z. For a second triangle, suppose x, y, and z are not all equal. More specifically, suppose for one triangle we have x=y=z=1 (a 2-3-4 triangle). And for the second one, suppose x=1, y=4/3, z=1 (a 2-4-4 triangle). Can you explain why two such triangles have the same area? I do not see how they would be equal in area. In fact Heron's formula would suggest that they are of different area.

There appears to be a confusion here. I never said the areas of the two triangles I used, a 2-3-4 triangle and a 2-2*sqrt(3)-4 triangle are the same. They obviously are not. The relationship between the areas of these triangles and the areas of their respective inner triangles are. When you did your own analysis, you didn't bother to choose a particular shape, you only took care the problem requirements were met. So did I.
Not being a mathematician, I am far from being rigorous though.
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RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-07-2017 11:39 PM

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