An Elegant Proof of the Shoelace Method

Proving the Shoelace Method using a useful property of matrix determinants.
Applets for Shoelace Method (Scroll to the bottom)
sites.google.com/view/matholi...

[@miguidieu06]

I like how you layed out the whole video. You made this obscure thing really easy to understand, and now I can confidently use the algorithm and understand what it is doing. Thanks you!

[@harrytsang1501]

It clicked as soon as you mentioned determinant. Thank you for your clear explanation

[@alyashraf848]

Extremely great video Thank you, you helps me alot ❤

[@MuhammadAnas_Official]

Nice explanation

[@alfredo970]

Really love this !!!

[@leducphuclong]

Thank you so much !!

[@mikaelengstrom6639]

Really nice explanation!

[@ChenHongming]

Glad it was helpful!

[@bahayesilyurt9433]

very nice

[@lucasloh5726]

if you made this a few months earlier you might have been able to submit it for #SoME2 (an event for mathematics on youtube)!

[@ChenHongming]

I'll time better for #SoME3!

[@cooldudelel7189]

Good video however i think it would be best if you made it clearer by explaining that since the third point is at the origin, it would not affect the answer as it is 0,0 and results in +0. Took me a moment to realise and I kept questioning why you dont repeat the first coordinate.

[@chonghow1804]

why is determinant of matrix equal to area?

[@ChenHongming]

the definition of the determinant comes from the inverse matrix and the inverse matrix is like a reverse transformation so you have to divide the “area” to restore the original 1 by 1 square grid. That is the deeper reason but in the video I go through the technical explanation

[@ericurt]

3:02 I don't understand why you said from (1,0) to (3,1), but then drew an arrow from the origin to (3,1)? what is the purpose of the red arrow?

[@zixiany]

🍋