Law Of Cosines I (visual proof)

This is a short, animated visual proof of the Law of Cosines using Thales triangle theorem and the intersecting chord theorem. This theorem relates the side of a triangle with the other two sides and the angle between those two sides. #mathshorts #mathvideo #math #trigonometry #lawofcosines #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #circle #thalestheorem #intersecting chords

To learn more about animating with manim, check out:
____________________________________________________
Background music:

[thiagot]

For anyone wondering about adjacent is 2acos(θ):


cos(θ) = adjacentSide / Hypotenuse

hypotenuse * cos(θ) = adjacentSide

hypotenuse is 2a, so:

2acos(θ) = adjacentSide

[boredomgotmehere]

Another wonderful and brilliantly visualized mathematical theorem. You’re one of a kind&mind! Thank you.

[jakobthomsen]

Great to see an application of the Thales / Inscribed Angle and Intersecting Chords theorems!

[mohammedmarhnine]

why didn't we see this kind of channel on top, gosh, you are amazing, thank u

[sumedh-girish]

Simply brilliant, it is these visualisations that make the math in my head usable. Thank you !!

[ll-lwvn]

Genius, my precal didn’t even explain why, she just show us the equation and let us remember it. This is so useful

[pardeepgarg]

1st
And thx for such a wonderful animation

Very nice animation.

What if theta is bigger then 90 degrees?

[minimalrho]

Is there a modern book that covers all the proofs of Euclidean geometry from say Hilbert axioms that has visuals as well (so excluding Hilbert)? It occurs to me that I've never seen a proof of Thale's theorem and the like.

[eipimath]

Thanks for sharing! I posted a short video on deriving the law of cosines, It should apply for all angles (acute, obtuse, reflex, negative). Hope to get your thoughts.

[harley]

I don’t get why the leg adjacent to θ is 2a cos(θ)

[kinggaming]

This will definitely help me in real life and pay my bills

[justunlocktheuniverse]

Just being curious, how do you make animation like this?

[Itsonlybecause]

How is leg adjacent to the angle tetha equals to 2a.costetha

[ckshene]

Sorry. This proof was due to Sidney Kung, which is incomplete. What is angle \theta is an obtuse angle or the circle you draw does not contain the triangle. While the general idea still works, but the reasoning would be a little of different. Please stop spread this incomplete proof. Additionally, many Proofs without Words share the same deficiency.

[khanohere-lpfp]

BHEEN KA LOWDY AGER TU TRIANGLE SHI BANATA TO MUJJA 2 GHANTA NA LAGTY SAMJHNY MA BAKI THANKU OSM VEDIO