4 DIFFERENT ways to prove Heron's formula

Your high school Math(s) teacher might not even explain to you how Heron's formula is derived, let alone Heron's original idea. This video explains 4 different ways to prove the Heron's formula.

Note:

This is a sort of experiment for longer videos. I am not exactly sure whether this would be helpful for both you and me, but let's see.

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#mathemaniac #math #heron'sformula #proofs #cyclicquad #geometry

Video chapter feature:
00:00 Intro
00:54 Using cosine law
02:30 Using Pythagoras theorem
03:34 Geometric proofs background
07:02 Heron's original proof
11:22 Modernised Heron's proof
14:19 Endcard stuff

[mathemaniac]

Don't forget to like this video and subscribe if you enjoyed this video!

[guyarbel]

Your channel is an underrated masterpiece :)

[ssssbw]

Very good conceptual video for defining Heron's formula from different ways.Thank you.
.

[interstallarscience]

Appreciable and easy to understand and interative

[rockinggirl]

Thank youuu so much for being short and precise!

[DhirajKumar-rxhi]

Kindly Prove the Area of Cyclic Quadrilateral
Which is exactly similar to Herons Formula but derived by an Indian Brahmagupta.
Area of a Cyclic Quadrilateral = sqrt((s-a)(s-b)(s-c)(s-d))
Where s is the semi-perimetre.

[dineshrathore]

Please complete Pythagoras method i can't understand

[tiagotrindade]

Thank you for the video! Your explanations are really good!

[nikitabrilliantov]

Really nice video!
The last proof inspired me to try to do my own (howewer, I have no doubt that someone figured it out before me)
There is a really nice property of cotangents:
If α+β+γ=π then

The law of cotangents:

We get:

Multiply both sides by s.
Consider the l.h.s.
sr³cot(α/2)cot(β/2)cot(γ/2)=

sr²(s-a+s-b+s-c)=
sr²(3s-2s)=s²r²=S²
The r.h.s.: s(s-a)(s-b)(s-c)
Taking sqare root of both sides we get the Heron's formula.

[directrix]

This is the best video on YouTube so far.

[mathig]

I used the law of cosines to prove it(without learning it's proof), and I was EXTREMELY hyped. Especially considering that I'm in class 9 😂🤗

[Ayushi]

Great proof sir 🥰❣️🥰


Love u from india 🌹💖🌹

[papkenhartunian]

I enjoy your lecture a lot. Could you let us know how many different ways are to calculate the area of a triangle? Further, how many different ways are proof of the Pythagorean theorem? I am researching these topics.

[abbasmehdi]

Now, through only yours video, i understood that maths is not limited and boring, it is researchal and much intresting than any other thing...thanks ....please produce more videos on arithmetic in deep..thanks you

[davidr]

And so
Area =
[(sum of 3 segments)
x(product of 3 segments)]
^(1/2)

[musical_lolu]

2:59 is actually a less explicit cosine rule with respect to the angle _B._ 😂

[peamutbubber]

virgin calculus/algebra fan vs gigachad geometry enjoyer

[Methuselah_]

What is the geometry of the transpose in dual space?

[dritans]

Very good job. Congrats.
It would be better when you autoplay algebra to write continuosly, not to cover previous results.
I wonder what software you use.

[sanaesana]

Thank you very much for your efforts but I don't understand English very well can you do the translation from English to Arabic 💙