How did Archimedes ACTUALLY calculate pi? Pi day 2021

[@theFINNISHmonster1]

Im personally really interested in history of mathematics (im sure im not alone) ,so this topic is perfect! More topics on history of mathematics please! :)

[@ciaranmcevoy9875]

That's great to hear pal! I'll most certainly be doing more videos on the history of maths.

[@MARCOSNAKANODANIEL]

I have watched this video like... 10 times already. Trying to understand each step. Thank you Very much

[@comic4relief]

Thanks for pointing out the proposition from Euclid. I have my own copy of Heath's Volume II, books III-IX.

[@gulnursaglam558]

Hi Ciaran, I like your videos very much! Thank you for spending the time to put them together. I would like to ask you a question about how to introduce pi to young learners. They learn that "Pi is irrational and pi is Circumference/diameter". For the definition not to contradict itself, either circumference or radius must be irrational. The circumference and diameter are finite, they start and end. So, question: How can something finite be represented by a number that has infinitely many decimal places? I know that there are some explanations to this phenomenon but I am interested to hear how you would explain it. Please keep making videos! They're very engaging and meaningful! Cheers:)

[@ciaranmcevoy9875]

Wow Gulnur, thank you very much! And what a fabulous question! I'm training to be a maths teacher at moment and that, without doubt, will be something I'd like to think about. I would love to make a video on that, thanks for the spark of inspiration.

[@ffggddss]

There's no reason that a finite number (in size) can't have a decimal representation that's infinite. You could, after all, ask the same question about ⅓, or ¹/₇ , each of which also has infinitely many decimal digits. But I gather that your concern is that infinitely many decimal digits represents an infinite sum, and that IS something of a puzzle - the ancients knew the concept as Zeno's Paradox. If you look that up (I'd suggest a Wikipedia search for starters), you should be able to find a better explanation than I could give here without a monstrously lengthy post (tl;dr). Fred

[@Mrpallekuling]

What error was introduced in the square root of 3 that Archimedes used? How much did that error affect the calculation of pi? Nice video, alas, fast tempo:)

[@kantaprasadsinha8025]

Thank u for clarity to a great extent. Deserve praise for your not mentioning even fractional numbet.. many were guessing how he calculated value of root over 3, India's s Baudhyan on sulvasutra formulated value of root over 2 in 800 be , following it, oondcan easily find out 1351/ 780. But other value ,it was difficult. Some conjectured p^2- 3x^2= 1. And -2, . Indeterminate second degree equation. Brahmagupta detailed I. Vargs Prakrit p^2 - n x^2 =1, . It was integer solution. In Diaohantine , this wS rational solution. However, want to know, how Archimedes calculated 265/ 153 for root over 3.requsr yo If u make calculations for every steps. Namaksr from India.

[@kantaprasadsinha8025]

Read decimal fraction number.

[@uubhi]

2:55

[@comic4relief]

11:03 Archimedes must have had tremendous thirst for knowledge.

[@ciaranmcevoy9875]

Absolutely!

[@endaodonnell]

Great video

[@bernatboschfolch]

how come the ratio of OA to AC is equal the ratio of square root of three? (4:00) How did Archimedes know that root was right? OK, I did a research and it can be proven by Pythagoras theorem that this length is the square root of three. But it is a gap for my taste in the video.

[@ciaranmcevoy9875]

I appreciate the feedback and interest Bernat. And yes, I had the same train of thought as you, and I found multiple papers and sources discussing how the Greeks and Egyptians calculated square roots. I decided that this is most certainly a video in itself as it's always fascinated me how they did it at all, so eventually I'll plan a video for that.

[@kantaprasadsinha8025]

Value of root over 3 for 1351/780 done by Baudhysna principle ( 800 bce in India). But 265/153 you have to recourse to x^2 - 3y^= -2,

[@whitewill25]

Mr MCEVOY do you have someone called Timmy in your class?

[@Fandom_wanderer]

Are u in his clash

[@whitewill25]

@@Fandom_wanderer i am😎😎😎

[@Fandom_wanderer]

@@whitewill25 I’m Timmy and mate

[@Fandom_wanderer]

My math teacher looks just like you

[@whitewill25]

My maths teacher is called mrmcevoy aswell 😂

[@whitewill25]

And he looks a lot like you aswell ciaran!

[@Fandom_wanderer]

@@whitewill25 I have a friend called Will Smith what a coincidence 😆😆😆😆

[@gojoXroman]

I have a friend called will smith too 😮😂

[@whitewill25]

@@Fandom_wanderer wait do I know u?

[@Jkauppa]

so they were stupid to have to calculate things, so sad

[@Jkauppa]

you dont have enough if you have to calculate, ration, pun intended

[@Jkauppa]

hard to listen, s-lackers

[@Jkauppa]

hand calculated piece-wise line-integral, multiplicates of the line segments, any function, circle y=sqrt(1-x^2), from the x^2+y^2=1 equation of circle

[@Jkauppa]

dont have to obey the rule

[@Jkauppa]

inscribed circle multicon, polygon, as the minimum, of the solution, greater than solution, that is as close as that many line segments can approximate the function shape, like area piece-wise sum approximation by a flat line through the center of the w/n wide segment, but same for line or circumference of the shape, function, circle, ellipse, any

[@greatguytv]

3.14159265