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RSS Feed for Wolfram Community showing any discussions in tag Geometry sorted by activeProving Pythagorean theorem using Trigonometry
https://community.wolfram.com/groups/-/m/t/3174364
I recently read that two students have proven the Pythagorean Theorem using Trigonometry.
I haven't looked at their proof, but the problem seems straight forward.
Consider a right triangle with sides a and b and hypotenuse c, and angle theta opposite side a.
Then the tan(theta) = a/b.
sine(theta) = a/c.
So c = a/sine(theta) = a/sine(arctan(a/b).
Using Mathematica:
a/Sin[ArcTan[a/b]] evaluates to Sqrt[1 + a^2/b^2] b
which is equivalent to Sqrt[a^2 +b^2]
In[1]:= a/Sin[ArcTan[a/b]]
Out[1]= Sqrt[1 + a^2/b^2] b
Am I missing something ?Frank Kampas2024-05-11T19:59:09ZFlat coordinates of algebraic Frobenius manifolds in small dimensions
https://community.wolfram.com/groups/-/m/t/3176299
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[1]: https://www.wolframcloud.com/obj/2271df93-f5ed-429d-aae3-dd9ef1a60ce2Johan Wright2024-05-14T16:21:33ZCode verification of immersed boundary techniques using the method of manufactured solutions
https://community.wolfram.com/groups/-/m/t/3175245
[![Daigram of using the method of manufactured solutions to validate a system of partial differential equations][1]][2]
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[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Cropped_Petoe_Wolfram_Community_Post_Cover.PNG&userId=20103
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[3]: https://www.wolframcloud.com/obj/31355ece-5e0a-45f8-88aa-4369a43519c9Márton Petö2024-05-13T18:34:42Z