Heron's formula visual proof | mathocube |

[@jhonnywhite1256]

Leaving a comment so the algorithm recommends this to everyone

[@Mathocube]

Giving a Heart because I like your comment

[@neuraaquaria]

That scaling part was genius

[@giap1707]

This is great visualization. I have hard time to understand the scale factor r(y+z) for the 3-rd right-triangle (z-r) initially. But it become clear once you have added the 4-th right-triangle (x-r) with scale rz. Logically, I think it might be easier to follow if order of adding 3-rd and 4-th right-triangle are swapped.

[@aguyontheinternet8436]

Yeah, it's pretty much impossible for him to explain why he's doing that without using words.I would recommend watching mathologers video if you still don't understand.

[@Kavoshgar-c2i]

How you found out the scale factor for the third right triangle?

[@sasankasekharmanna3193]

Our hero had put some real thought into this.

[@shahriyar.tahsin6661]

this deserves more views

[@JuanIgnacioAlmenaraOrtiz]

Just beautiful!

[@chrislloyd5415]

I actually love the formula AREA=perimeter*r. Only two quantities involved not three! The size of the inscribed circle depends on the ratios of x,y,z as well. Fascinating. I think there is a slight missing element that could have been mentioned in the second element where you scale up the triangles and put them together into a rectangle. How do you know you can get a rectangle? Because these three triangles involve exactly half of the internal angles of the triangle and so add up to 90 degrees.

[@sushilasawriya3040]

V v good 👌👌

[@User-54321n]

Genius that u are ❤️. 🙏

[@WilliamChen-qg5cj]

This is so intelligent!

[@adityaparadkar6947]

skillfully made, everything has been given a thought

[@prasadborse2161]

I didn't understand a single thing but it's awesome to watch it 😂

[@muqtarjamaegal6071]

Math is visual please questiont rule calculus make animation calculus if you can you are amazing like 3blue 1brown

[@Mathocube]

I will do my best.

[@anandthakur4616]

Greatest of all time

[@TRJK]

Fantastic👍

[@anishkumaranjan]

That's why I've subscribed you dude. You're amazing

[@mshirazbaig6055]

Beautiful.

[@Kavoshgar-c2i]

How you found out the scale factor for the third right triangle?

[@sonalichakraborty6830]

Though your concept is copied I highly praise you for your efforts and for the dedication to do the needful

[@hamedfaraj]

I really love this , and I am glad to find it

[@caperider1160]

Best visual proof

[@mrminer071166]

This would be a cuter animation -- simpler and more elegant -- if you UNWOUND the three triangles like beads on a string, so that all three bases were collinear, and all three triangles of the same height.

[@SiddhaBhaiya]

Explain your comment

[@mrminer071166]

@@SiddhaBhaiya Have a look at Dudney's famed square/triangle hinged dissection. kzbin.info/www/bejne/gYHdooWer9aEqNE and do a similar animation with Heron's formula as a dissection into three triangles. With bases on the same line, and all three triangles with the same altitude.

[@muktamalakar5771]

Thanks for the video man. Excellent 👌👌

[@Mathocube]

Glad you liked it!

[@shahriyar.tahsin6661]

this video is so much under rated

[@BeastSuperGamerz]

Very Good Bro

[@hanniballecter0]

What do you mean by "Scale it" and how we scale traingle like what did you do abd ehat is scaling do you have a resource please

[@Mathocube]

It means that you have to keep the angle the same and multiply its side by a constant. i.e. if you have a triangle of sides 3,4,5 then if you want to scale it with a factor of 2, then multiply all the sides with 2 and the sides of triangle becomes 6,8,10

[@riyahnajim]

Brilliant

[@hanniballecter0]

Can you explain the scale in another KZbin video what is scaling in minute 1 what z (x^2+r^2)^1/2?

[@Mathocube]

Sure

[@georgemaxwell3997]

Cute, but inadequate. When adding the third triangle to the second, how do you know that they have equal hypotenuses?

[@ISAACK----.....-------611]

if i may ask which software is this

[@faketypho4392]

You are incredible

[@user-fajv-feibb]

Please explain me the scaling part

[@bobmichael8735]

what software do you use for this video?

[@Mathocube]

I use adobe after effects

[@hanniballecter0]

From where did you get this proof what is the book please ❤

[@Mathocube]

I found this on the internet.

[@God-nx7ji]

how did you divide the triangle though??

[@psiphixium3919]

This is gold

[@spinbulle5312]

Can you provide the source or the link from where you got this proof.

[@jordangertino1867]

They were up to some crazy stuff thousands of years ago

[@thephilosophyofhorror]

Subscribed.

[@torbjorn_aadland]

To me it's not clear from the video why sxyz can be replaced by s(s-a)(s-b)(s-c). What have I missed?

[@Destroyer_10]

S=x+y+z and a=x+y so s-a=x+y+z-(x+y) which equals z; b=y+z so s-b=x+y+z-(y+z) which equals x; c=x+z so s-c=x+y+z-(x+z) which equals y; and if you add them together you get x+y+z=(s-a)(s-b)(s-c)

[@davidbrisbane7206]

The visual proof is easy enough to follow after a few views, but it takes about 20 minutes to remember how to construct this visual proof, and it is mostly memory, as nothing about this visual proof is intuitive, apart from computing the area of the triangle. Also, given a triangle, we need to assume that we can actually inscribe a circle in it that touches each side at a tangent. Yes, this can be proven, but it is not obvious that this is true.

[@fermatcoachingcentre7659]

Bro .. Can you tell me what kind of software you’re using to draw such lines and circles

[@Mathocube]

I use adobe after effects

[@nehakaushik1838]

🤟🤟💯

[@Syed_M.Hammad1]

I didn't understand (scaling)

[@ByasKushwaha-c1i]

Why you scale it

[@luciousaritoriuscastus]

❤

[@God-nx7ji]

and how is xyz = (s-a)(s-b)(s-c)???

[@sandeepbait8428]

s = x+y+z & x+y=a (s-a)= x+y+z-(x+y) = z same (s-b)=x, (s-c)=y Therefore xyz=(s-a)(s-b)(s-c)

[@sandeepbait8428]

❤❤❤

[@hanniballecter0]

How x + y + z = (a+b+c)/2

[@Mathocube]

Because 2x + 2y + 2z = a + b + c

[@TheDHemant]

One has to pause video and study. But the question is how do you think of it!!!

[@Mathocube]

arey kehna kya chahte ho 😂

[@royeditz18]

😂😂😂​@@Mathocube

[@taginpaktung639]

Not understood.

[@ikhrasashaa65]

Im gonna brb