Law Of Cosines II (visual proof)
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- čas přidán 4. 05. 2023
- This is a short, animated visual proof of the Law of Cosines using the Pythagorean theorem. This theorem relates the side of a triangle with the other two sides and the angle between those two sides.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
This animation is based on a proof from Timothy Sipka in the October 1988 issue of Mathematics Magazine (www.jstor.org/stable/2689363 ) page 259.
For another visual proof of this same fact check out:
• Law Of Cosines I (visu...
#mathshorts #mathvideo #math #trigonometry #lawofcosines #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #circle #pythagoreantheorem #obtuseangle #acuteangle #angle
To learn more about animating with manim, check out:
manim.community
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Music in this video:
Elegy by Asher Fulero
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
I love binging your videos! Keep it up!
Excellent! Thanks for watching :)
Keep up these amazing videos!!
I’ll see what I can do. I’m over two years in and at some point I’ll run out of visual proofs I find interesting :)
Nice little visual proof, but I think that the "algebraic manipulation" that change a sin into a cos would have been worth explaining. In fact, it feels like the heavy lifting of this proof is in the algebraic manipulation.
The sine doesn’t become a cosine. Sine squared plus cosine squared results in 1. The only algebra is the square of a difference.
@@MathVisualProofs I see. For me though, Sin square + Cos square equal 1 is more a Trig identity then just algebraic manipulation.
Nonetheless, very nice visual proof. 🙂
@ Thanks! I do say "algebraic rules along with the pythagorean trigonometric identity" to indicate what needs to be done - so I agree that is more than algebraic manipulation.
Now this becomes hard to forget!
This is awesome
Glad you like it!
In the obtuse example was side a for all the base or soecific part of it ?
You should have pointed out the sin²+cos²=1. Many viewers may not know trig identities.
I do mention you need the "pythagorean trigonometric identity" so that people can search that if they aren't aware.
And it is weird because in your second you added a right triangle and proved it like that i mean it does not make sense because you are solving for a different triangle now not an obtuse triangle so how both are related?
I really liked your work and explanation. Can you help me with the name of the program you are using for the explanation
I use manim for this.
Amazing❤
Thank you!
One day the importance and need of VR and Augmented Reality will be realized in Schools and Universities
Beautiful. What do you mean when you say this is equivalent to Pythogarean theorem though ? If we didn't have it in the first place we wouldn't be able to prove the law of cosines, no ?
You can prove the law of cosines without the Pythagorean theorem.
very good....
Thanks!
why is Pitagorean Theorem called by the mathematician's name and i almost never see this one called Al-Kashi's law of cosines?
Yes, PT should be called "Right triangle theorem". Unfortunately it is how it is.
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You must cote Al Kashi for this theorem as you cote Pythagore !
우와..........
👍😀
Kind of speeded through. If you slow down a bit and added a few more algebraic steps, then the video would be great.
Noted. Thanks.
It is not called the law of cosines , it is called Alkashi's theory originally made by one of the greatest arabic mathematicians. I think we should give the honor to his name and not change his theory's name.
Irrelevant, and neither is a theory.
@@friedrichhayek4862 i meant Theorem but u got the point
2:08 why does b*sin(pi-theta) = b*sin(theta) ?
This is a fact about the sine function, which measures the y-coordinate on the unit circle after rotating angle theta. So if you instead rotate pi-theta you have the same y-coordinate.
This was confusing since I thought of it like theta minus pi, and not like pi minus theta.
@@TheEGod. theta-pi doesn’t give you the right identity.
@@MathVisualProofs Yeah thats why I said I was so confused. Since I was thinking of something inccorect.
@@TheEGod. Oh! I see. :)
Software name please?
Manim. It’s in the description of every video.
I still don't understand why it's Pi minus the angle alpha
That is the supplementary angle. Two angles that create a straight line must add to 180 degrees or pi rads
Love it❤❤❤
Thanks!
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I understand some of these words.
Start with those and branch out to the others 👍😀
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It's a nice video, but calling it a visual proof seems like a stretch.
I mean, it is a published "proof without words." So in my mind, it's a pretty good visual proof. I added some commentary, but I think it stands alone too.
A little too rushed
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It’s not a fully “visual proof” since you included “algebraic manipulation”.