Part 2 of proof of Heron's formula | Perimeter, area, and volume | Geometry | Khan Academy

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Showing that the expression in part 1 is identical to Heron's Formula
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[@getatme625D]

Heron's a hero! Sal is the most patient being on the planet!!

[@DynestiGTI]

How did people work this stuff out 2000 years ago... boggles my mind!

[@AshishMishra-kn2ui]

🙄🙄😇😇

[@pendawarrior]

@@AshishMishra-kn2ui ok

[@aguyontheinternet8436]

Well, they already had the formula, they were just simplifying

[@PivotSideEffects]

this made a scary amount of sense

[@fsponj]

Yeah

[@thanaa6401]

I see no sense here just algebraic manipulation

[@nisargchaudhari5184]

Thank you for this proof of Heron's formula

[@Heligoland360]

That was beautiful!

[@ad2181]

Excellent derivation to create the difference of squares, three times. Thanks for showing this Algebric trick for reductions.

[@saahilthukral]

Thank you so much Sal. It helped A LOT in my Math Research Paper!

[@nickputkaradze1181]

I haven't seen something as beautiful as this for a while.

[@shotono3286]

almost as beautiful as your pfp rero

[@nickputkaradze1181]

@@shotono3286 Ah, man of culture here

[@danrain12345]

Mind = Blown

[@kushshrivastava6894]

Sir, you are great

[@icommentfornootherreasonth8773]

its so beatiful that something i can understand so easily i would have never came up with myself. It isn't really complicated but the first person to discover it (heron) was a real genius

[@mrhatman675]

I mean these formulas basically came out by luck by playing with the numbers and already known formulas

[@icommentfornootherreasonth8773]

@@mrhatman675 yeah thats what i mean!

[@lomertamahon1]

You got some talent. That was outstanding.

[@carlossoto9511]

beautiful!

[@lastminuteproductions691]

O M F G!!! i was a little far behind on math in school from a vacation, and i came to watch how is the Herons Formula implemented, and i got stuck to the previous video and this one omg!!!!!

[@redsalmon9966]

It also proofs that maths is beautiful

[@eshansharma9458]

I am becoming good at math!! I prooved this thing myself on my notebook all my self!(here to check if I was wrong but I was not!)

[@nageshp4964]

Please send part 1 of this.

[@noelsojr]

Yeah what fuck.. I love math

[@OmerMan992]

WoW! I have never been that fascinated by mathematics. THANK YOU!

[@danieldddddddvise]

What is that software you use? I need something like that as well, it could save me so much ink and paper :O

[@andrewd3899]

That was beautiful.

[@trivugia1416]

Wow amazing result

[@adventureboy444]

Wow. It's crazy how you can simplify stuff by overcomplicate it

[@VineetKumar-uh4ut]

Amazing explanation sir!! Lost hope at commencement of video but gradually caught the idea of it..... wonderful!! Thanx😆

[@ritwikkanojia3655]

This is the longest, most complicated, most genius proof I have ever seen

[@navindraarjunaabeyesekera7864]

Excellent

[@mehmetcanbicen12]

Thank you so much, that video was really useful for me and for my term project.

[@unoriginalusernameno999]

As Richard Feynman once put it: The mathematical laws of nature are not complicated. It's just a lot of it!

[@TheOlgaStudio]

Wow, that was truly helpful! Thank you so much

[@shivamramdhani8151]

Explanation🙏👍

[@sakshikumari5621]

It was awesome🙃

[@ifiaz]

excellent explanation... nice work!!! keep it coming...!!!

[@A010795]

So colourful...

[@SkSk-so8nm]

Sir you are great

[@SkSk-so8nm]

Too great sir

[@sankalpmishra5416]

it is a brilliant" proving" site

[@shreyaskumar7658]

that was awe inspiring man great

[@xigong4729]

Awesome formular

[@TheSheepyCell]

Nice

[@QuanNguyen-eg8zw]

so much math its awesome

[@AdityaPatel-yx2dk]

This is awesome!

[@PreCalculusRocks]

That.. was... AMAZING! thanks alot! :)

[@mrhatman675]

This proof was huge!!!!

[@MartianSpore]

Bravo good sir!

[@ahmedbaig7279]

It was beautiful. Let me say that I am also prepared to present one presentation on Heron's Formula. Arecyou ready?

[@manishjois5538]

Very nice.

[@michaelsharpe5112]

very impressive

[@RealMcDudu]

excellent

[@vikramdhimmar3895]

thanks

[@aaaagggg7262]

Hello sire. Can you tell me which program that you use to write. Thank you for cooperation

[@UnderscoreZeroLP]

I assume you are not a native English speaker, here is a better version: "Hello Sir, Could you tell me which program you are using to write on the screen? Thank you"

[@ShashiKant-cm8dw]

This proof is brilliant , outsanding But I want to ask you that ic this was prooved by heron or you yourself thought it If you thought it yourself,,you arebgreat sir

[@neerajrattehalli9347]

Beautiful

[@redjr242]

For some reason KZbin won't let me type the up arrow so just imagine that the ampersand: & is the power symbol. sqrt(c&2 / 4) = sqrt(c&2) / sqrt(4) = c / 2 Therefore sqrt(c&2 / 4) = c / 2.

[@MuiYuDoTheLoo]

hi

[@111222333444R]

Hairy but satisfying.... where have i heard that before?

[@rishavbhagat9408]

awesome

[@gavenhollandsworth9201]

so many variables!

[@shreyaskumar7658]

only three variables are there

[@div_yam2304]

Not that many

[@div_yam2304]

@@shreyaskumar7658 actually no x^2 and x are mathematicaly different variables

[@shreyaskumar7658]

@@div_yam2304 God, this was way back long. Anyhow, I think I am correct - if a function contains both x^2 and x, than they are simply giving different outputs for the same input.

[@andrewfeng3403]

elegant

[@asalad083]

Sal, you are the MAN.........:-)

[@jerfersonmatos28]

Legal cara, eu aprendo matemática ao mesmo tempo que melhoro meu inglês

[@someperson5137]

How can anyone dislike this?

[@HimanshJainYTube]

hey i want to know that which software is you using for making the screen black and writing upon it with multi colours

[@div_yam2304]

Paint with a black background works for me

[@austinmacintyre3697]

Woah...

[@chenadam6339]

Khan, How did you actually know how to algebraically manipulate the equation to the desired result? Just like 09:12 -b =a-2b ? I really want to know, or is it e procedure need to memorize? Thank you

[@unoriginalusernameno999]

Its called creativity. Also called thinking out of the box. Maths is like a sandbox Universe in which you could throw and smash and create and destroy new blocks from existing ones. Once you start playing you could then just do about anything. That's why great Mathematicians aren't just mathematicians. They are sometimes artists. Sometimes they are good at sports. Some even play bongos! There is no memorising in Maths. The fundamental rules apply and they stay same throughout the Universe.

[@onesandzeroes]

Crazy stuff. But it works! :-)

[@danielche2349]

what you just said was the same thing that this kid in my geometry class says a lot. is that you?!! O.o

[@jonas59222]

Trying to tell myself, that someday I might understand this...

[@Joseph-yx5mt]

Same here. XD

[@jerfersonmatos28]

I think now you two understand it

[@CraftyThink]

@@jerfersonmatos28 Lol same

[@biplobhimu]

😮

[@danielche2349]

from his last video.

[@PivotSideEffects]

how dose he operate the calculator?

[@aaa_ron]

Thank you, I have brain damage jk nice video made a lot of sense still don't get how people have this amount of creativity

[@danialdunson]

these videos without sound are great

[@UnderscoreZeroLP]

lmao I think you have broken speakers...

[@rajvirmanku1216]

I

[@xyliahvortex661]

Take a shot every time he says "squared"

[@jetpaq]

that algebra had a BIG foot suit on! HAHAHA!! but it was so AWeSOME! man this guy is unbelievably smart!

[@hellfigter12345]

How can c^2/4 = c/2 ? pliz help :)

[@chesslover1768]

hellfigter12345 it's quite simple=> c/2 =c /2 =>(c/2)^2 = (c/2)^2 =>(c/2)^2 = c^2/4 =>c/2 = √(c^2/4) Proved!☺☺

[@123lol1234know]

wow haha thanks... i just earn 20 extra credit from watching this ^^ thanks lol nice job

[@prosoftenterprises]

@Pctech4uproductions He is using Paint since ,you can see multicolor but he doesn't show the toolbar above.

[@danielche2349]

and this one.

[@aguyontheinternet8436]

AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

[@kubyoindiya3269]

C L A S S I C 😂

[@akshatrakesh69]

too many vars...

[@SEnergyable]

cool, now let's find a job where I'll calculate the area of triangles all the time and I'm fine..

[@strategen9124]

SEnergy engineering, and life (if you are a curious person who wants to understand geometry of common mathematical objects found in this amazing nature that we humans happened to be in) :)

[@scriptkiddie7485]

so you are not simplifying it at all, just writing it in a way that looks simpler... so I guess you are simplifying it

[@Sooper35]

Holy shit that was beautiful. CitizenKaneClapping.gif

[@GndmMkv]

this proof is so LONG!!!