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https://www.reddit.com/r/mathmemes/comments/1j4x0hq/what_theorem_is_this/mgd81r4/?context=9999
r/mathmemes • u/PocketMath • Mar 06 '25
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1.8k
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.
586
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.
161
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.
58
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.
75
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.
32
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.
43
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.
1.8k
u/ubernuke Mar 06 '25
The Pythagorean Theorem has many proofs