A brief history of geometry I | Sociology and Pure Mathematics | N J Wildberger

[@gabenuss3063]

I work in 7-12 math education, and tutor out-of-state students whose curriculum includes concepts from the history of geometry that I didn't really explore in my formal education. Thank you, sir!

[@pickeyberry4060]

Video Content 00:00 Introduction 02:50 Earliest theoretical result in geometry 06:09 Early geometry is applied! 12:35 Greek period: pure/abstract geometry 17:27 Greek period: applied/astronomical 19:57 Indian geometry 22:01 Islamic/Arabic period(800-1500)

[@phiarchitect]

We are truly on a path of discovery with mathematics, both collectively and individually. I wonder how the future will look back at this time. The global standardization of syntax and grammar of mathematical symbols is a significant achievement. But we are really just beginning, aren't we?

[@antizephdaniel7868]

Hell No! If you can create a bubble universe for yourself and continue feeding yourself with lies for the next 20 years of your life, then this is the beginning of the great things that you'd experience in the "future".Every man who is not interested in this nonsense should possess the ability to exit this reality. Why can't I build my own bubble and say this year is 1947.Is this not similar to what certain children are doing right now?Your stupid reality with Mr fear monger the rat and Mr Beer belly the greedy pig? It is a choice if you want to end up in a cartoon graveyard.

[@jdp9994]

Your presentation of the sequence from Pythagoras to Heron to Brahmagupta caused me to jump to wondering: what about general cyclic polygons. So I came across the early 2021 paper of Dulio and Laeng, generalizing Heron’s and Brahmagupta’s equalities to any convex cyclic polygon. They find the solution by focusing on the way incircles of triangles (of a certain triangulation) divide the sides of the triangles (and of the polygon) to find a consistent extension. After so many years of hard work by so many, a relatively simple geometric solution revealed. Now, what about extending these to polyhedral volumes and higher dimensional analogs?

[@ManleyCates]

You are an amazing speaker and I cannot thank you enough you are helping my high schooler get through geometry via history thank you thank you thank you

[@sharonjuniorchess]

How do you map stars? Its an interesting problem to ponder how one would even get started and where one would start? I still remember marvelling as a small child at the night sky on a little island just off Auckland as my father pointed out the southern pole and the constellations. I believe that Norman is referring to the Dunhuang Star chart @7:05: en.wikipedia.org/wiki/Dunhuang_Star_Chart A fantastic lecture even though it was a brief history it was "as seen through a mathematicians eye" which was pretty mind blowing in what it touched upon. Like alighting upon stepping stones in water that are actually columns going fathoms down.

[@antizephdaniel7868]

Before you map stars maybe you should consider asking yourself if your "eye" is TRULY real or it is complex. What do the stars represent, considering that what you see as the sky is a Riemann Sphere and the primary algebra has been taken as E8 by the goons lol?

[@FigureOnAStick]

Appreciate the video! I have a hard time studying subjects without context, so having the history of geometry laid out so clearly really helps me understand the math so much better!

[@thephilosopher7173]

Thanks for going into the history. I never cared for math and failed it in high-school. Richard Feynman sparked my interest with his lecture, and got me to pick up Euclid's The Elements. But the hardest part about it is that there's no context to how or why they figured out these propositions. This helps with that and gives me a chance to learn it better, so *Thank You!*

[@gauravbisht4649]

Hello Teacher *N.J. Wildberger* Wow! Sociology and pure mathematics. Thank you.

[@bakhtiyorkuliev5293]

Lovely lectures. Cheers from Samarkand.

[@goldthumb]

Thanks a million from Toronto

[@lachenmann]

I tend to disagree with the notion that geometry and mathematics have their origin in commerce. It seems that we cannot think of the past other than in modern terms, as if their worldview was no different from ours. I think that nothing can be further from the truth. I susbcribe the thesis of Italian mathematician Paolo Zellini (Google his books, they are amazing) about the sacred origin of mathematics (after all 'mathema' is not just any knowledge, but the knowledge that was given to the initiates) in ancient cultures, in particular in Vedic, Greek, Sumerian and Egyptian cultures. I hope you find this notion interesting, thank you for your excellent work with this channel.

[@TheRosyCodex]

Very interesting, I remember elsewhere he had mentioned that the drawing of sacred symbols or construction of temples would have been an early motivator for the study of geometry

[@samisiddiqi5411]

It most definitely is. In fact, we only discovered the Pythagorean Theorem trying to Square the Circle, which were symbolic of Heaven(Circle) and Earth(Square) in Ancient Times.

[@robertmotsch7535]

Excellent presentation. You at your finest!

[@jryer1]

There is so much left undiscovered in spherical and solid geometry. Very sad state of affairs what's being taught today, some of which I question qualifies as mathematics. When I think mathematics, I inevitably think 2 or 3D geometric objects.

[@subhamjaiswal3677]

At 14:53 You mean Thale's was a teach of Euclid, right?

[@RichardSouthwell]

Great video. Why do you say Pythagoras's theorem is the most important one ?

[@TheRosyCodex]

I think it's because, as we move into geometry via coordinate systems, it is central to being able to measure distance (or QUADRANCE) between two points

[@denniswhalebone2583]

Great video, thanks.

[@chjxb]

Great video. Plato is a great guy.

[@nascimentomoreira9668]

This was amazing, thanks for share your knowlogy!

[@ekszentrik]

Standing in front of a whiteboard adds 1000 points to online classes cred and detracts 500 points from popsci cred.

[@JB-kn7ig]

Its really nice to see you still uploading, thank you for this. I always wanted to ask you, do you think that your spreads from rational trigonometry would better for creating 3d programs, like video games or 3d modelling? If you have a chance to reply, thanks - but thanks anyways for the videos :) Cheers from Kansas

[@dsm5d723]

You used subtend correctly. Euclid would be proud.

[@primenumberbuster404]

Geometry is my favourite!!!

[@TheRosyCodex]

Geometry is the muse of mathematics, arithmetic the work horse, and Algebra the King

[@santerisatama5409]

Always learning deep new stuff from your videos, thanks. 3-4-5 triangle defines orthogonality, and quadrance 9+16=25 is "phibonacci". Fascinating!

[@OKMathh]

Thank you!

[@3zdayz]

Spherical geometry doesn't really represent natural or axis-angle rotations either... although a location on a sphere can represent a direction, the angle around that direction to determine the final orientation is omitted. Using azimuth/elevation or lat/long sort of coordinates to determine a direction doesn't help with the math of rotations either, and finding a new axis-angle for a rotation rotated around another axis-angle rotation.

[@rujackswing618]

There is a History Mathematics on YT That Says that Meso & Egypt did not Have a Formula for the Triangle until the Greeks gave it to Us... All the Monuments the Arabs & Egyptian Built in Europe, Asia & Africa... It is a Shame.. Peace..!!!

[@joanferreira3896]

thankm you

[@MrGerryodonothing]

A Chara, it isn't often these days that I come across one who might take notice of a comment/question, that a viewer or even a subscriber might ask. I have a bit of a conundrum going on for a while now and I'm nearly there on the solution, but not being a "mathematician" I will be subject to ridicule should I reveal it. WHy is there 360 degrees in a crcle. Derivation is what i'm looking for, is mise le meas.

[@bubbajones6907]

I heard the platonic forms and all of geometry is derived from the Sun and Moon, which is the intersection of two circles of the same size forming the vesica pisces. This is where we get the saying, "God's will be done on Earth as in heaven", and is why where we live is called the "middle yard" in Old English. The flag of Israel is based in this.

[@TheDavidlloydjones]

Good professor Wildberger seems confused. Geometry is written in sand. Waving your arms around in the air is not geometry, that's topology.

[@njwildberger]

@David Lloyd-Jones Sadly my office has run desperately low on sand.

[@mariadoroftei6416]

Thank you!