Little explorations with HP calculators (no Prime)

04072017, 10:19 PM
(This post was last modified: 04072017 10:20 PM by Han.)
Post: #149




RE: Little explorations with the HP calculators
(04072017 10:04 PM)Gerson W. Barbosa Wrote:(04072017 09:26 PM)pier4r Wrote: About the proof. I learned the hard way that showing the correct result may be a coincidence, while proving it is something different. If you just "prove" with a result it is like a proof by example, so, no proof. 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 234 triangle). And for the second one, suppose x=1, y=4/3, z=1 (a 244 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. The two solutions you presented are simply two special cases of the problem because you have not presented how the general case may be reduced to either of the two special cases you presented. Graph 3D  QPI  SolveSys 

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