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.
Sources:
manuscriptsandmore.liverpool.... (Euclid’s photo)
famous-mathematicians.com/her... (Heron’s photo)
www.famousmathematicians.net/... (Pythagoras’ photo)
brilliant.org/wiki/cosine-rule/ (Cosine law proof)
en.wikipedia.org/wiki/Heron%2... (Selected Heron's formula proof)
Other useful links:
www.mathsdoctor.co.uk/revisio...
www.quora.com/How-do-you-deri...
ckhtrevor.quora.com/Brahmagup...
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
#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!

[@interstallarscience1376]

Ok I did sir

[@DhirajKumar-rx8hi]

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.

[@ssssbw6337]

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

[@guyarbel2387]

Your channel is an underrated masterpiece :)

[@mathemaniac]

Wow, thank you!

[@rockinggirl0610]

Thank youuu so much for being short and precise!

[@mathemaniac]

Don't think this is short haha, but thanks for the appreciation!

[@rockinggirl0610]

@@mathemaniac no haha i dint mean short as in length of the video but people usually draaaaag the entire theory by repeating things and giving unwanted details

[@tiagotrindade1819]

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

[@siddhikabra1579]

So thankful for your channel!!!!!!

[@mathemaniac]

Glad it helps!

[@mathig7470]

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 😂🤗

[@prostatecancergaming9531]

This proof was in my 9th grade textbook as an exercise. It’s not a complicated proof since it’s mostly algebra.

[@interstallarscience1376]

Appreciable and easy to understand and interative

[@mathemaniac]

Glad that you enjoyed the video!

[@nikitabrilliantov6996]

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 cot(α/2)+cot(β/2)+cot(γ/2)=cot(α/2)cot(β/2)cot(γ/2); The law of cotangents: r=(s-a)/cot(α/2)=(s-b)/cot(β/2)=(s-c)/cot(γ/2); We get: r³cot(α/2)cot(β/2)cot(γ/2)=(s-a)(s-b)(s-c); Multiply both sides by s. Consider the l.h.s. sr³cot(α/2)cot(β/2)cot(γ/2)= sr²(r*cot(α/2)+r*cot(β/2)+r*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.

[@alvaromatos3661]

you just saved my life

[@AJ-et3vf]

great video. thank you

[@moularaoul643]

Thank you!

[@DhirajKumar-rx8hi]

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.

[@directrix8844]

This is the best video on KZbin so far.

[@mathemaniac]

Pretty sure this isn't the best video on KZbin, but thanks for the compliment!

[@directrix8844]

How old are you?

[@mathemaniac]

I have (vaguely) answered this question on the comments of my other video "15-year-old did mathematical research?! What was my thinking process back then?"

[@DhirajKumar-rx8hi]

Masterpiece

[@dineshrathore9871]

Please complete Pythagoras method i can't understand

[@2false637]

Came from Quora, you rock!

[@Ayushi4646]

Great proof sir 🥰❣️🥰 Love u from india 🌹💖🌹

[@mathemaniac]

Thanks!

[@sohumsharma2892]

I liked the proof by law of cosines

[@musical_lolu4811]

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

[@abbasmehdi2923]

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

[@mathemaniac]

I would probably not produce videos in arithmetic, because it is not very interesting and completely misses the point of mathematics to concentrate on arithmetic, but I will definitely produce more interesting math videos.

[@abbasmehdi2923]

@@mathemaniac ok

[@peamutbubber]

virgin calculus/algebra fan vs gigachad geometry enjoyer

[@subhradipporel9598]

that was nice

[@mathemaniac]

Thanks!

[@Methuselah_]

What is the geometry of the transpose in dual space?

[@wojciechswiderski1532]

cool!

[@msconcepts]

Animation Software?

[@davidr1781]

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

[@SuperYoonHo]

subbed

[@papkenhartunian186]

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.

[@dritans7334]

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.

[@mathemaniac]

Will consider this suggestion - just that there are too many "previous results" that I need to show on screen, and I am not sure which ones to cover. As for software, I want to keep it a secret for now:)

[@christopherellis2663]

Hẹrọn ( eta, omega) hair awn

[@amirk6290]

👍🙏

[@interstallarscience1376]

Seeing it again lol.

[@sanaesana5251]

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

[@mathemaniac]

Thank you for the appreciation, but honestly I don't know any Arabic... you might be able to get Arabic translation by clicking the settings on the video, and then on the subtitles section, you click "Auto-translate", then you can see the Arabic version. See if that helps!

[@sanaesana5251]

@@mathemaniac 💙OK I will try thanks😊

[@marleenday8782]

heroin

[@marleenday8782]

i meant to say herobrian

[@yasiryousuf4437]

@@marleenday8782 you could edit the comment

[@marleenday8782]

GROW UP

[@pepperoniboy57]

what did you mean by this

[@ferashamdan4252]

سرق الاغريق علم الهندسه من المصريين والبابليين. كفى كذب وتدليس. لم يكن يعرف الاغريق حتى الحروف والكتابه الا لما تعلموها من الكنعانيون وابناء عمهم الفينيقيون.

[@DhirajKumar-rx8hi]

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.