Pi is IRRATIONAL: animation of a gorgeous proof

cosx expansion should be x² not x otherwise great as usual.

Off with his head! 😂

I'll be back here later when I get to the upper level

the first puzzle:
log10(2) is irrational:
10^u/v = 2
10^u = 2^v
5^u.2^u = 2^v
the right side and the left side have different primes because 5 is not on the right side, which breaks the uniqueness of prime factorization
log7(8/9) is irrational:
7^a/b = 8/9
7^a = (8^b)/(9^b)
7^a = (2^3b)/(3^2b)
3^2b * 7^a = 2^3b
again, this breaks the uniqueness of prime factorization
for the second log, I think that claiming you're rational is like saying you're smart, rational guys don't say they're rational, so I think it's irrational

Ok, so pi is irrational. What about proving it is non-algebraic, i.e., that it is transendental?

Shouldn't the second term in the expansion of cos(x) be x^2/1×2, not x/1×2?

Just asking for a friend: what happens in the concluding piece if A is omega, or omega plus one i e if you go hyperreal, or surreal?

how is Kate Bush "Babushka" related to pi? both irrational?

love, true poetry

wow

nice, pure poetry or will be when you finish the details

I kind of liked grading too, Marty, it gave me an opportunity to help and encourage students.

can i put 'mathologer algebra merit badge" on my ECA?

I like the infinite descent, but you can (if you want to) do it in a single step using the "minimal criminal" method (voire Matuchek or others).

Note: PLEASE don’t use green and yellow for anything important; some of us have red-green color blindness. 🙁

Okay, but one of your videos is a proof that e and pi are transcendental. But how does this differ from being irrational? Are all irrational numbers transcendental, or only some of them? Are all transcendental numbers irrational, or only some of them?

the first log is irrational, because ∀v,u∋Z 2^v≠10^u, because 2 is a prime, and 10=2*5, so dividing both sides by 2^u gives us 2^(v-u)=5^u, but that's impossible, since 2 is even, 5 is odd and v-u is an integer, so2^(v-u)≠5^u. QED

Hi Mathologer, You show that pi is not a rational number. The way I see it, if you start with a point in space and start spiralling from that point you are eventually going to end up off track, Now if you adjust your position about 2 True Vectors you will be able to correct your orientation. I show this with Quad Step 288 spherical order system. Now this shows the spherical geometry of a Pine cone or a Pine Apple or the 200 seed pattern of a strawberry. It gives incredible symmetry that has never been shown ever by Mathematicians, It will be nice if you could give folks your down to earth analysis of this Hierarchical system that uses groups of 4 angles about a fixed vector without having to use the mathematics of your wandering pi about ring centre points.
There is also an interesting connection to the Harmonics of Music that people have shown to be related to this Quad Step 288 harmonic system.

I love the shirt

Circles are perfectly round, and this the continuity of its surface is infinitely round

I love the (ho)^3 shirt where can I get it it's so funny

”However; here’s a bit of bad news.” At these words, I saw The Matholantern’s eyes (pardon the pun) really LIGHT up 🎃😅.

nobody seems to have noticed that the series formula for cos x, should have x squared as the first power of x, not x to the first power. Or somebody must have seen this.

I know I am wrong but I need to understand. Isn't the number of ALL the numbers between 0 ans 1 uncountably infinite? So we should be able to count down from 1 to 0 with ininitely many steps, right? Where am I wrong?
If anyone could explain I would be soo glad, so thank you in advance

The cameraman shouting nonsense in all these videos is really disatracting and annoying. But you sir are brilliant, thank you.

This was surprisingly easy to follow; even for me, who took Intermediate Maths in high school, and stopped there. Thank you for making this beautiful proof accessible even for amateur mathematicians, like me. 🙂👍🏻

Der Inhalt ist sehr interessant. Der Ton ist etwas dumpf.

In the cos expansion, the ^2 is missing!

Awesome video, though. I didn't even know a proof of the irrationality of e ^^
I wonder if you could make an equally accessible video for the transcendence of pi.

666k views? 🤔

Pi may be irrational, but it is also delicious.

A circle is the equation πr² a sphere is πr³. A circle is the ring or symbol of "marriage" for it is to last or continue 'forever. A form of infinity you and your spouse's rings. This is because the circle can be split equal three times across before the calculation into each section becomes "askew" of the shape. In this the formula to go around the circle must be forever, or it would have an end. No circle has an end. Even our longitudinal lines are off in this sequence. 0° , 180° 359.999999999999....° approaching the zero, north or south pole. 3.14 is just the approx yet it has every single numerical value or sequence. Yet data, or datum, is not meta until it has a store value assigned to it. Every address you lived at by number will occur somewhere, yet only you would know it.

Good, nice proof, I read the one that is in Spivak's book and is quite oscure, this one seems a bit more natural but certainly continued fractions are not that popular nowadays.

Ayyy pi dayyy

I just realized his shirt foretold Christmas invading Halloween all theses years ago

log10(2) is irrational.
2=10**u/v [where u and v are two integers]
or, 2**v=10**u
or, 2**v=2**u.5**u
or, 2**(v-u)=5**u [(v-u) is an integer by closure property]
but 2**(any integer)!=5**(any integer) since (even no.)**(any integer)!=(odd no.)**(any integer)

why does 25 DEC = 31 OCT on his t-shirt? I don't understand.

great proof and the yawohl must have been prompted by the black T-shirt and the German accent! 　怖い 😵‍💫

My proof is chord based as the diameter of all circumferences is the last and largest chord found inside a circle. 3.14159ect. Is a ratio that is numerically based only, whereas the circumference has numbers which describe its diameter the value of a circumference ratio is 1.5702. There are 100 ratios to a circle’s circumference. They are found by both simple division of a limited numbers of values between 1-10 and by use of chords. Also, the corruption of time by the addition of fractions of a second is the second proof. Minus all decimals in the clock Hours, Minutes, and Seconds are all chords which are ratio of the circumference. This explains the end of General Relativity as the relationships is fix and is Intentional Relativity.