Parallelogram Area from Side Angle Side

This is a short animation showing a standard fact about how to find the area of a parallelogram using the lengths of the two sides and the angle between them. This fact will be used in future videos showing the AM-GM inequality and the Cauchy Schwarz inequality (and possibly others).

#area #trigonometry #parallelogram #angle #sideangleside #geometry #visualproof #math #manim

To learn more about animating with manim, check out:

[paralyion]

A single synapse fires each time i watch your videos, thank you for single handedly keeping brain activity alive ❤

[creeperbinary]

YOU ARE THE BEST. I tried
to proof this formula by using this stuff.

Let draw a diagonal that not effect the angle of theta.

Then use sine formula that a×b×sin(theta) over 2 than multiply both sides with 2 than you get a×b×sin(theta)

[vennstudios]

I mean... Looking how it works when it moves like as it morphs


It is definitely a sine function
Since like 90 is the maximum and 0 is the minimum and which function has
A maximum at 90 and minimum at 0
It's the sine function

[kalvincochran]

Also serves as a visual proof of taking the cross product or determinant of a matrix right?

[SirDoBig]

I love these videos i just want to know how they make these

[Jff_Kng]

I suppose that the music volume is auto set by yt but for some reason the audio is peaking a lot in my phone and it's not usual that

[dougr.]

And a)(b sinθ = vector a cross vector b (cross product is a DIRECTED area)