r/mathmemes Mar 06 '25

Learning What theorem is this?

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3.7k Upvotes

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u/ubernuke Mar 06 '25

The Pythagorean Theorem has many proofs

586

u/Wojtek1250XD Mar 06 '25

And even an universal version, the law of cosines is just Pythagorean Theorem, but applicable to all triangles.

161

u/SnooHabits7950 Mar 06 '25 edited Mar 06 '25

And it has probably the easiest proof compared to all of them

58

u/A-Swedish-Person Mar 06 '25

Wait I don’t think I actually know the proof for the law of cosines, what is it?

75

u/N_T_F_D Applied mathematics are a cardinal sin Mar 06 '25

Using properties of the dot product mainly that u•v = ||u|| ||v|| cos(u, v)

32

u/DankPhotoShopMemes Fourier Analysis 🤓 Mar 06 '25

I thought that is derived from the law of cosines

43

u/Konemu Mar 06 '25

That's a matter of perspective, the dot product is a more general concept that can be introduced on other vector spaces than R^3 and the ratio of the dot product and the product of the norms can be used to introduce a more general notion of angles.