MathHistory3a: Greek number theory

The ancient Greeks studied squares, triangular numbers, primes and perfect numbers. Euclid stated the Fundamental theorem of Arithmetic: that a natural number could be factored into primes in essentially a unique way. We also discuss the Euclidean algorithm for finding a greatest common divisor, and the related theory of continued fractions. Finally we discuss Pell's equation, arising in the famous Cattle-problem of Archimedes.

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Education

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• History
• of
• mathematics
• UNSW
• Pell's
• equation
• Archimedes
• Cattle
• problem
• continued
• fractions
• Wildberger
• triangular
• square
• numbers
• primes
• Unique
• factorization
• fundamental
• theorem
• arithmetic
• Euclid
• perfect
• Mersenne
• coding
• security
• nextprime
• Euclidean
• algorithm

[fennyLOL]

WOW I am greek you know... but in Greece, in our schools never teach that to us..!!! too shame... Well done!! And thank you, that I learn from you, my "history".. Ευχαριστώ

[jtaglenava]

thank you for sharing your knowledge!!

[tuitionplus]

@wiredboy27 yes...the best i've ever seen...agree

[mickstarify]

@Kurtlane i believe its (2^n - 1)* 2^(n-1) where 2^n -1 is prime, you forgot the minus one in the exponent

[Kurtlane]

At 29:29 - 44, statement

"If 2^n-1 is prime, then (2^n-1)x2^n is perfect"

Is it "if" or "iff," i.e is the opposite:

"If a number is perfect, then it can be expressed as (2^n-1)x2^n, where 2^n-1 is prime?"

also true?

Thanks.

[archieh70]

@wiredboy27 If it's keeping you back from completing your thesis for a Nobel prize in Maths, don't watch it. It's for a History of Mathematics course. It was good of them to upload it as they didn't have to.

This is a University lecture. People arrive late as they do in all Universities. As long as they don't come in shouting and singing, nobody cares.

If this video is annoying you, you may want to watch some videos on English sentence construction and punctuation.

[peterhi503]

Wildberger, excellent work as usual.

[UndeadTheta]

Wow that theorem about perfect numbers was beautiful!

[wiredboy27]

Arrive on time idiots and move the camera when he goes to the other board. dude you should edit this even more or just take it down altogether and do it properly in your own time in a comparative study with other schools. You should watch delawaremath, I dunno I thought you were like one of the best in the world, I can't believe you're explaining square numbers to some grubby teens, no wonder you need to quote the book, this stuff is obvious. too obvious.

[celal777]

love your videos . keep them coming.