Area of a parallelogram

[@1234567S4]

Thanks again Dr!! I love watching and learning from you. I’m a high school math teacher, and guess what?! I’ll be teaching Calculus next year, which is a dream come true. I’ve always wanted to teach it! I’ll be referencing your channel and blackpenredpen to my students. Thank you for all you do man, I just love it!!!!

[@madhavpr]

I never really paid attention to the geometrical meaning of determinants and the relationship between volume of parallelopipeds in R^n and the utterly horrible Laplace expansion formula. Today, I just sat down with a notebook, pen and a cup of black coffee, listed the basic properties a determinant function should satisfy 1) Linearity in each column 2) Antisymmetry 3) det(I)= 1 and derived the horrible Laplace expansion formula for the 2x2, 3x3 and the 4x4 case. Turns out, the formula is not mysterious at all. 😀 I think it's not so difficult to extend these to the general nxn case, provided we keep track of the number of switches/permutations of indices. Finally, I understood why the signs alternate to calculate the determinant via cofactor expansion [+, -, +, - etc] 😀 Oh btw. Great video Dr Peyam !! 😀

[@puatengyap4173]

WTF AREA

[@ffggddss]

Yes, I was loving how that works *_both_* ways ;-) Fred

[@dexter2392]

WTF allegedly stands for "want to find", XD

[@BabyXGlitz]

شكراً جزيلاً دكتور پايام

[@thegamingsamurai6860]

Very helpful, thanks Dr Peyam

[@hustler3of4culture3]

I've been wondering for a while now. I will incorporate this into my explanation of detA.

[@kgregor7]

I only know this version: Donaudampfschifffahrtsgesellschaftskapitänswitwe, your version is new to me 😀 And as always very nice video!

[@KnakuanaRka]

Gregor K What the heck is that jaw-cruncher of a word?

[@kgregor7]

K1naku5ana3R1ka I will try to translate: it is the widow (witwe) of a Danube (Donau) steam ship (dampfschiff) society (gesellschaft) captain (kapitän)

[@jonasdaverio9369]

I don't think it is particularly clearer in English. The only addition are spaces...

[@kgregor7]

Jonas Daverio leaving out all the details, the long german word means “captain’s widow”. Clear enough?

[@plaustrarius]

Excellent!!! and we get parallelepipeds for free now basically!

[@chongli297]

Can you relate this to the Jacobian? I think it is so amazing how we can use parallelograms to approximate the area of the image of a square under some mapping and then perform a change of variables to make our integral easier!

[@drpeyam]

Yeah! There’s s video on the Jacobian where I explain precisely that!

[@nayyarabbasi4697]

Excellent videos

[@Chris-ye7ip]

Can you make a video in your finest Österreich Dialekt?

[@neilgerace355]

This really is a pretty special result ... Can it be generalised to other polygons and polyhedra?

[@newtonnewtonnewton1587]

Nice video D peyam as usual surly i like it that is the answer of ur quistion in the end of ur video

[@jonasdaverio9369]

60 views? Was this video unlisted?

[@drpeyam]

Yeah, it’s unlisted! It’ll be up in a week or so

[@skeletonrowdie1768]

haha firster than first

[@allyourcode]

This is my favorite explanation of det. I would love to see why this works in higher dimensions. I have seen a good explanation in 3D from Krista King, but what about 4D and higher?

[@hemanthkotagiri8865]

Can someone name those long words he said in the beginning? I'm a bit curious

[@pedrocusinato02]

Hemanth Kotagiri all right tnks 4 watching

[@drpeyam]

Metaphysicotheologocosmolonigologie

[@koenth2359]

Parallelogram Diagonizability Metaphysico-theologo-cosmologicology Donaudampfschifffahrtselektrizitätswertsgesellschaftskapitänswitwe, if I heard it correctly, meaning something like 'widow of the chairman of a society for valuing electricity on steamboats on the Danube')

[@spockfan2000]

NISOME (NIce+aweSOME) !

[@jamiewatt6814]

Ah so that's why |u . (v x w)| gives the volume of a parallelepiped

[@tomatrix7525]

Awesome

[@sabilal-rashad]

0:30 😄😄

[@thelastherobrazilproject113]

Awesome!!!!!

[@papsanlysenko5232]

2:48 2/3 ?

[@patricksalhany8787]

Pneumonoultramicroscopicsilicovolcanoconiosis. Yes, this is actually a word.

[@drpeyam]

Hahaha, there’s a GREAT story about this! I was playing Trivia with a friend at the pub, and the bonus question was “How many letters does the longest English word have?” and he then added “Haha, whoever can spell it right gets 100 extra points!” And my friend got it right!!!! The host was baffled

[@patricksalhany8787]

Haha! Nice Dr. Peyam!

[@FlyingOctopus0]

Here a different visual proof: i.imgur.com/Q3MAaNy.gifv it is more direct. I transform an a*d size rectangle into parallerogram and b*c sized rectangle. I use the shear operation, which preserves area and some cutting with translation.

[@IlTrojo]

Parallelograms are still less interesting than Zur Elektrodynamik bewegter Körper...

[@anniamatthews6803]

wow