Oldest Unsolved Math Problems Solved After Eons

[@alabamaal225]

It is actually possible to "square the circle" using a compass and straightedge, using the following procedure: 1) Mark a point on a circle's perimeter. 2) Rotate the circle 360 degrees (one full turn), tracing out a straight line segment. The resulting line segment is equal to the circumference of the original circle. (Imagine a can rolling on its side.) 3) Using the compass and straightedge, bisect the line segment into a half segment. 4) Bisect a half segment into a quarter segment. 5) Again using the compass and straightedge, construct a square with each of the sides equal to the quarter segment. The resulting square will have an area equal to the original circle. It won't be possible to determine the exact length of the square's sides since Pi, which defines the circle's perimeter, is an irrational number. Nevertheless, the constructed square is a valid geometric representation of the squared circle. Neat, huh? Except for one problem: I cheated. You see, I didn't use just the two instruments, a compass and a straight edge, but also used a rotating marked circle. The rotating marked circle qualifies as a third "instrument", which is against the rules. Pi is also a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. Because Pi is involved, it would take an infinite number of steps to "square the circle" using only a compass and straightedge, making such a solution impossible. Sorry.

[@ItsMS_62]

What that photo for Legendre 😂

[@orly4672]

It's an unfinished caricature of him. It was meant to exaggerate his features in a comical way, as caricatures would.

[@renatofernandes1086]

@@orly4672 It's the only surviving image of the man, so it is still used.

[@coopa_troopa0192]

how does this guy not have millions of subs! this channel has crazy good quality

[@ThaSPAWN]

well, he has more subs than there are people interested in maths in the World, so there's that...

[@lumbersnackenterprises]

144 is one of the coolest numbers in all the ways it tends to show up

[@kloklowewe4874]

No?

[@lumbersnackenterprises]

@kloklowewe4874 It's 12 squared as well as 12th on the Fibonacci Sequence. It showed up as the answer for the smallest fifth exponent thing as part of the Eulers thing. It's the 2^4×3^2 which I think is neat. How is it not cool?

[@monishrules6580]

I like 21

[@lumbersnackenterprises]

@monishrules6580 21 is also rad. I like to think of it as the bigger part of 121 (11^2).

[@yuvrajganguly]

Fermat basically said CBF......

[@badpiggs]

CBF like in geometry dash?

[@DavidIsFrenchTemp]

​@@badpiggsI think

[@camelsouttahere.]

Click between frames?

[@DKDexter999]

In a way, isn't Euler's sum of power's conjecture, and Fermat's last theorem ... "sort of" the same?

[@isavenewspapers8890]

Yes, that conjecture was intended as a direct extension of that theorem.

[@roneyandrade6287]

Is this a re-upload?

[@MrSeanMDickinson]

Brilliant! Thanks 🖖

[@ThoughtThrill365]

Glad you liked it!

[@e-pluszak9419]

<a href="#" class="seekto" data-time="492">8:12</a>, yeah, but if for one value of B this ratio approaches 1 so it does for any other as lim x→∞ (x / (ln(x) - B_1)) / (x / (ln(x) - B_2)) = 1, to make any sense of "optimal value of B" you need to define some more strict way of comparing π(x) with x/(ln(x) + B)

[@isavenewspapers8890]

See equality at 8:47.

[@marcelob.5300]

Great as usual.

[@fahrenheitwastaken]

Amazing!

[@richardgratton7557]

Fermat is pronounced « Fur-ma »

[@Robi2009]

<a href="#" class="seekto" data-time="335">5:35</a> - gotta ask: why that map in the background is in Polish :D?

[@isavenewspapers8890]

Just a random video of a map. The specific choice of language doesn't seem to be relevant.

[@CalBruin]

The name is _Noam_ Elkies not "Noah"

[@Liquid_Pain]

ooo cool, i like learning about maths :P

[@Little-pluto-behind-neptune]

nice

[@LeoStaley]

The way you keep mispronouncing fermat's name

[@faisalsheikh7846]

Are you an real person or an AI?

[@alexwarner3803]

Since it is narrated by a text to speech, likely AI content. It seems apparent based on the blatant mispronunciations and typos put into the TTS software. E.g. Noah for Noam. Same inflection for everything. Similar issue in another video. No good.

[@isavenewspapers8890]

@@alexwarner3803 How much trolling until you get tired?

[@ThoughtThrill365]

@faisalsheikh7846 real person