10 Amazing Math Facts You Never Learned In School
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- Опубліковано 26 бер 2023
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Prepare to have your mind blown as we dive into the fascinating world of mathematics, exploring lesser-known facts and concepts that you won't find in a typical classroom. In this video, we'll uncover intriguing topics like palindromic numbers, spherical geometry, hyperbolic geometry, the Tower of Hanoi, the Mandelbrot Set, the Birthday Paradox, and more!
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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.
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no
nah
hi
To add on to the birthday paradox, once u have 75 people, the chance that 2 share a birthday is already almost a gurantee already(≈99.97%), which is only about 1/5 of the 365 possible days
My class have like 50 and no one shares a birthday
in my class there were only 14 people and 2 of them share a birthday
@@curerose0630 some schools sort students by birthdays
My class 24 people and 2 people share a birthday while me and another classmate are off just by 1 day of our birthday
well for the birthday problem to work the distribution of people born in each days of the year must be equal
Optimal strategy for Towers of Hanoi with n disks (if present), from source peg A to target peg C using auxiliary peg B:
1. Solve optimally for the top n-1 disks (if present) from A to B (2^(n-1)-1 moves)
2. Move bottom disk from A to C (1 move)
3. Solve optimally for the top n-1 disks (if present) from B to C (2^(n-1)-1 moves)
Total: 2^n -1 moves
Its quite a nice example to illustrate proof by mathematical induction.
All that’s missing is the base case n=1, which is quite clearly true(1 disc only needs 1 move, and 2^1-1 is 1) but must still be included in the proof.
@@Ninja20704 the n=1 case is just where there’s nothing for steps 1 and 3, since for n=0 there are no disks to consider.
@@marcusscience23 yes, n=1 would just be step 2 and that’s it.
It's a good way of understanding recursion as a concept, particularly in relation to computer programming. Mind you, you need a computer language which is powerful enough to allow you to repeatedly call a section of code in a nested fashion, e.g. Pascal.
@@markkreissl1544 I actually made a python code for this:
def toh(n:int, a, b, c):
if n>0:
toh(n-1, a, c, b)
print(a, ‘->’ ,c)
toh(n-1, b, a, c)
I think vsauce + 3b1b + Numberphile is enough to cover all of these topics on UA-cam, love seeing these things talked about more :)
your feelings are irrational
I'm a twin ... when I was young, the probability for me to have someone in the same room with same birthday was close enough to 100% that it didn't matter 🤣
i saw the banach-tarski paradox video by vsauce and that broke my brain beyond repair
What's an anagram of Banach-Tarski?
Banach-Tarski Banach-Tarski
0:00 It's also a repunit.
Great content! Keep it up.
Nice!
The only ones I didn't know were the first one and the last two.
5:19 it's not finite, it's in infinnite pieces.
Exactly. Banach-Tarski only works when you split it into infinite pieces, which size loses meaning. As long as you’re splitting them into finite pieces it doesn’t work.
He means a finite _number_ of pieces. The pieces themselves obviously contain an infinite number of points.
@@PureExile True, but the pieces aren’t “solid”. Their infinite points are disconnected, separate by infinitely small gaps. If you break it into pixels, every pixel will have points, no matter how small the pixels get, but individual points are still separated, they’re just infinitely close. Because of this, volume loses meaning and isn’t well defined, and only because of this can they achieve the paradox.
The Banach-Tarski Paradox animation made me laugh so much
Why is always the Mandelbrot fractal more popular than the Kochs snowflake fractal? :( I think it looks way more dope!
Mandelbrot set looks more like a photo material
"MATH FACTS YOU NEVER LEARNED IN SCHOOL"
Number 1: CALCULUS
It's like being that kid in primary school that shouts x^2=4 is also -2 or in high school asking "What about the irrational solutions"
... I mean they're interesting facts, the clickbait just annoys me
You should have added Trevor's (from Grand Theft Auto V) "blablablablababla" audio clip at 5:50
I work in a bar, just 6 of us yet 3 of us have the same birthday and another guy we work with has a brother who shares our birthday. I wouldn’t know how to work that probability out even missing out the other guys brother 😱
I would suspect that if 11^2 = 121 and 121^2=14641 , then 14641^2 would be the palindrome 1248421 or something. But its not, its 154281241 which feels totally random and is kinds weird
121^2 is 14641
here's a fun fact: the digits of 11^n will be the same as the numbers in the nth row of pascal's triangle. At least until 11^5, where the numbers in pascal's triangle are more than a single digit.
In another base, 11 in that base to the power of 8 could be 142181241
14641^2 = 214358881
12421^2 = 154281241
14641^2 = 11^8 is indeed palindromic, except you can't represent it in decimal as such. It's 10^8 + 8 10^7 + 28 10^6 + 56 10^5 + 70 10^4 + 56 10^3 + 28 10^2 + 8 10^1 + 10^0. If you allow an extended form of decimal notation where each column can contain an arbitrary quantity instead of just the digits 0-9, this property becomes obvious. If you move to higher bases this becomes clear as well. For example if you let a-z be 10-36 then 36^6 base 35 is 16fkf61.
121^2=14641 which is also the 5th row of pascal's triangle. in fact:
11^0 = 1
11^1 = 11
11^2 = 121
11^3 = 1331
11^4 = 14641
11^5 = 161051 seems to break the rule but:
11^5 = 10^5 * 1 + 10^4 * 5 + 10^3 * 10 + 10^2 * 10 + 10^1 * 5 + 10^0 * 1
so it has the fifth row of pascal's triangle but a little hidden due to the limits of a base 10 number system (in base with more digits the pattern would continue)
the reason the powers of 11 encode pascal's triangle is because pascal's triangle encodes the binomial coefficients, and:
11^n = (10 + 1)^n
the reason pascal's triangle encodes the binomial coefficients is also very interesting:
consider (a + b)^n. we can expand this with exponent laws to:
(a + b) * (a + b)^(n - 1)
now lets say that (a + b)^(n - 1) = (c * a^(n - 1) * b^0 + d*a^(n-2) * b^1 + ... + z * a^0 * b^(n - 1))
so now we can use the distributive property to get:
(a + b) * (a + b)^(n - 1)
= (a + b) * (c * a^(n - 1) * b^0 + d*a^(n-2) * b^1 + ... + z * a^0 * b^(n - 1))
= a * (c * a^(n - 1) * b^0 + d*a^(n-2) * b^1 + ... + z * a^0 * b^(n - 1))
+ b * (c * a^(n - 1) * b^0 + d*a^(n-2) * b^1 + ... + z * a^0 * b^(n - 1))
= (c * a^n * b^0 + d*a^(n - 1) * b^1 + ... + z * a^1 * b^(n - 1)) + (c * a^(n - 1) * b^1 + d*a^(n-2) * b^2 + ... + z * a^0 * b^n)
combining like terms:
= c * a^n * b^0 + (d + c) * a^(n - 1) * b^1 + (e + d) * a^(n - 2) * b^2 + ... + z * a^0 * b^n
so the rule to get the coefficients of (a + b)^n given the coefficients of (a + b)^(n - 1) is the same as the rule for getting the next row of Pascal's Triangle given the previous! (i.e. adding together the numbers adjacent to each other)
If you want to read about the cultural and social (and of course the math/science) implications of zero, there’s a terrific book called “Zero: The Biography of a Dangerous Idea” by Charles Seife. I highly recommend it. It has some technical chapters, but most of the book is about how zero impacts things like religion and culture. Very cool!
I covered the Four-Colour Theorem with my students last year! Fascinating and easy to understand, and you can see why it led to so much development in graph theory!
Thanks for reminding me of the Birthday Paradox … I’m starting a probability unit with my students in a few weeks, and that’s a great way to start it!
Nice meta-joke with mispronouncing “mispronunciation”. 😂
The Mandelbrot Set makes me instantly think of Holly Krieger!
Anyway, good video!
Nice video! Hope to see more of theese :D
1:45 "Also comes in handy as an eye chart,"
-- Johnny Wayne and Frank Shuster, "Rinse the Blood off my Toga".
5:14 Time for some misproNOUNciation! Lol, the irony!
i love these facts
Wow, a bosonic tower of Hanoi 🤪
Mandelbrot set is the most beautiful thing of mathematics ever found.
Learning how to solve problems like 1^x=2 or x= π! opens a whole new world of math.
for the four colors theorem ( 3:07 ) are regions allowed to have exclaves? [Ex: Kaliningrad-Russia] i assume no since there are situations where it would not work if that were allowed
How does he explain the 6 degrees of separation?
Bro the euclidean triangle gon' humbled
5:00 What’s the probability of that though?
That animation made my day
5:12 Speaking of mispronunciation, you mispronounced "mispronunciation", which has no o before the u :)
The birthday one is funny to me because in my class of 26 people, there are me and 2 other people whose birthdays are the 21st, 22nd and 23rd of April
5:00
how do u know that someone in room was not born on 29th feb
How to Tell, that I'm a math nerd: I acually knew every point on that list XD . Good Video tho!
Why did the chicken cross the Mobius strip? To get to the same side. 🤣
3:37 whydid the animation fall through itself
I actually learned about all of those in school. School's cool.
I'm doing a speech about fractals in my speech class
Jus
Why
@@maalikserebryakov because their fun
I have had someone in my class share my same birthday three times in my life
I like your exposee. Next time could you just help me a bit, by dividing for subject, for example by counting out or change color? It would help me know what I am listening too. Thank you for the offer from your sponsor
"10 Amazin MATHS Facts!!"
Me: Why am I watching this?
Me: Why am I still watching this?
Still Me: Why did I watch that?
5:46
It is true.
I learned all of these facts only by learning Maths on UA-cam
5:46 literally ROFL :'D
Great episode, but in the end of the birthday problem you said "the odds get higher" when I assume you meant "the chance gets higher". When the chance gets higher the odds get lower, right?
Segments are not triangular and you can't say triangle can be more than 180 degrees
What the hell was that? 3:37
What does the 'B' stand for in Benoit B Mandlebrot?
Benoit B Mandlebrot
3:33 This problem you say is "Tower of Hanoi" was said to be a Mathematical problem from Varanasi (Benares; have you ever heard of this city?). George Gamow explained this in his book "One Two Three . . . Infinity". You better, have a look at this book.
Prior to Mathematics, it would be better for you to improve your knowledge of History - if you intend raking up historical facts.
Wow. 🎉
Assuming birthdays are uniformly distributed, and ignoring leap years, you need 253 people in a room before it's odds-on that one of them shares _your_ birthday. This is just the smallest natural number _n_ for which (364/365)^n is less than one half.
Isn't a Möbius strip just a torus that's been squashed a weird way?
No. A torus is orientable and has no boundary, whereas a Möbius strip is non-orientable and has a boundary so the two objects are clearly not topologically equivalent. However, there is an operation on a torus called taking its quotient which interchanges the two coordinates that define its surface parametrically; the quotient of a torus is indeed a homeomorphism of the Möbius strip.
There is an unofficial Roman numeral for zero which is N
Nice 👍
I think I watch too much math video, I already heard of all of them.
5:13 - "Time for some misproNOUNciation..." You mean, "misproNUNciation"! 😅
Cool video. Still can't figure out what is going on with the thumbnail!
"The shortest distance between 2 points on a sphere is along a great circle connecting those points." True if they can be connected by a great circle, but many can't - they can only be connected by small circles: for example, two points at the same latitude on Earth cannot be connected by a great circle - their shortest-distance connection is along their common latitudinal arc (a small circle).
Any two distinct points on a sphere can be connected by a great circle. A great circle is the point of intersection with the sphere's boundary and a plane passing through its centre. For any pair of points we can define such a plane (for example, in standard Euclidean 3-space, define vectors from the centre to each point and take their cross product; this will be normal to the plane). Latitude is an artefact of fixing a point on the surface of the sphere as a pole. Choosing a different pole corresponds to rotating the coordinate system.
@@davidgillies620 Now, that's interesting, and thanks for pointing that out. I was looking at, for example, Blackpool, UK (53.8167° N, 3.0370° W) and its connection with Leeds, UK (53.8008° N, 1.5491° W) via conventional lines of latitude, not realizing I was still thinking 2-dimensionally in terms of orthogonal planes. But you are quite right: if we simply use those 2 points as a hinge and rotate the plane around the axis connecting them, we find that any number of planes might include those 2 points, including the plane passing through the centre of the sphere (we can approximate by calling Earth a sphere on this scale as we can approximate by equating the latitudes of Blackpool and Leeds), which does indeed form a great circle when intersected with Earth's surface. I think what tripped me up was that, when we do this, the arc connecting the 2 points is no longer the shortest possible distance traversable along the surface of the sphere. Thanks for making your explanation so clear by involving vectors originating at the sphere's centre. Well done!
@@jamesmunroe6558 The arc along a great circle between two points on a sphere is always the shortest distance. Great circles are geodesics on a sphere which _by definition_ have extremal length. Small circles, by comparison, have non-zero geodesic curvature (which is a concept from Riemannian geometry) and therefore the distance between two points on a small circle is larger than the great circle distance. This is a non-trivial subject that you don't normally encounter until some way into a maths or physics degree, and can be a bit counterintuitive.
@@davidgillies620 Once again, I really had to think this one through. In doing so, I realized I'd fallen prey to a misconception I've provisionally named the Mercator Fallacy. It arises because, on a Mercator map, the shortest distance between two points lying on the same (non-equatorial) latitude is indeed along that latitude, which corresponds to a small circle, whereas the line following the great circle is (on the Mercator projection) longer. It took some visualizing to realize that, when applied to a spherical surface, the great-circle arc is shorter because it's the orthogonal projection onto the spherical surface of the tangent to the sphere that also intersects the vector lying midway between the two vectors you mentioned from the centre of the sphere to each of our endpoints, whereas the latitudinal line (provided it's non-equatorial) involves a detour. (I was able to look up and understand the definition of geodesics, a term I had only previously heard in the context of a "geodesic dome" and other Buckminster-Fullerian shapes but, although my understanding of and enthusiasm for math is quite good for a layperson, being a programmer but not a math major, the concept of extremal length is still, I fear, beyond me.) Thanks for the education.
i don't understand how did we find 23 for the birthday problem
"Time for some mispronounciation"! Yup, so let's start with mispronunciation
I was 3 people away, my guess was 20
I think fun facts are not nesesary in term of learning, just using them as examples so school ignored.
no chapters?!
Talking about the Mobius strip and then not mention its actual application in industry as a way to distribute wear to both sides of belts, thus increasing their lifetime. Missed opportunity there.
Thanks
But this is not an engineering channel
In my opinion, it is best to expunge pure mathematics from all discussion of “applications”
It distracts students too much from the foundational issues they need to work on like getting good at integrating difficult functions, improving their skill in proof, in solving equations,
Too much emphasis on muh applikayshuns is simply a trap
@@maalikserebryakov That is just plainly ignorant. I'm a pure mathematician through and through, with a master's in algebraic geometry and cohomology on schemes. And I think this is one of the coolest things about the Mobius strip.
I'm not saying everything needs an application. But when a cool one exists, ignoring it in favor of putting "purity" up on some pedestal is just wrong. Math is supposed to be at least a little bit fun. And unexpected connections are always fun.
Adam Neely but maths
So IIIIIV wouldn't be zero? WTF
CMIIW, for minute 2:10, wasn't Roman Numeral were invented before the number 0 so it doesn't have 0
oof, Manim is not happy today
1 is a palindrome, and when you square it, the result is ALSO a palindrome!!!
Fun information , but the transitions are very abrupt
WYSI video length
Any power of 11 is a palindrome
Ok
10th
Who one knows about iit jee
Its not true what u say
Spherical geometry IS NOT like Earth
Earth is sphere in some space, but spherical geometry is the space curved like a sphere
I am sure it wasn't 10
:)
I read the title as: 10 amazing meth facts
😠 For a channel promoting mathematics, your use of ‘ton’ is somewhat peculiar. A ‘ton’ of research? Clarity in the use of language is essential in conveying meaning to an audience. Foggy language is one major reason why students fail to understand what is being taught.
I too am an enemy of foggy language
shall we masturbate together over how precise our use of language is
Click-bait title! I have taught Mathematics for 20 years, after 12 year in industry.
[TLDR: some items many not be appropriate at High School, and more likely you forgot the lesson for the 'surprise', they are used to emphasis a TEACHING POINT/SKILL not as an END TO THEMSELVES]
[Edit]: This video indicates special cases that have WOW, but the underlying Mathematics is frequently taught, and the extremely level of it is the result of a long JOURNEY; we have to choose which to show. A better title "The Special case you forgot from Mathematic Lessons". Encourage students for the Extra-curricular programmes - not necessarily Olympiads. As you may see, these are the results of more common concepts.
[Edit] PLEASE Support your Mathematics Teachers, we have a lot of SKILLS and TECHNIQUES to teach, many of these examples are either the result of a special case or require a LOT of work to get to.
I hope your Maths (guessing US) teachers contact you to highlight when some of these were shown in class. Many teachers do these little side projects to introduce these ideas; depending upon the classes I've done intersecting
* produce patterns from numbers --- used within proofs, particularly identifying the implications of factorising
* great circles creating angles, expanding and changing - Mercator Projection and why maps work
* number systems... BINARY, HEXADECIMAL, NEGATIVE, COMPLEX NUMBERS, numbers
* mobius ... done this regularly, try predict the outcome; try 1/3 of the way from the right edge, ant walks along the strip (PHYSICS - an analogue for 1/2 integer spin)
* four colour theorem ... use to extend to 3D for colouring touching surfaces [I don't remember but will have to look back at my notes] (use to extend to large numbers, Grahams number is a map colouring upper limit that we do not know the top end but we know it end in a 7... linking back to patterns in the sequences of numbers), interestingly also the difference between Venn and Euler diagrams in Set theory; also the concept of PROOF - as mentioned - EXHAUSTION (yep feeling this right now)
* tower Hanoi ... development of a strategy (varying number of discs - the Myth of the Buddhist monks who are doing 64 rings, and when they finish the world will end, 1 a sec --> more than 4 billion years...
* birthday Paradox ... agree probability is anto-intuitive, link to the "Monty Hall" - "Goat problem", developing the analysis of problems by considering scale, i.e. rather than 3 doors. Also, further analysis (Monty did NOT ALWAYS make this offer!)... Birthday is linked to dice matching et games, this becomes the conclusion - PLENARY
* banartaski Paradox --- got me here, but have done the odd lesson upon hole counting on Topology, including the thought experiment of turning a sphere inside out; the coffe mug solution to 3-houses connected to 3-utilities problem --- including my planar solution - CLUE: the houses are not points!
* mandelbrot -- used to demonstrate the popular vision of fractals, but we regularly make Serpenski triangle and other patterns of simple rules; including patterns of even numbers in Pascal/Cardano/Yung Hui Triangles --- including the misappropriate names --- Mandletbrot itself requires COMPLEX NUMBERS and ITERATION, i.e. a lot of time! By the way I think it was the 1960'/70's that Bernot Mandlebrot (died since 2000) was able to use a computer to find the iterative limits of z²-1 for all point in the complex plane - so not intrigued "FOREVER". Koch Snowflake and Serpenski Triangles teach more about the ideas of infinitissimals, limits and the difference between convergence and divergence.
[All the above are off the top of my head, no further research or notes referrals, most teacher's could probably easily tick off half!]
Each one listed I have used as examples or end of term "fun exercises" to link back to content taught earlier in the term -- as much of this would be, YOUR VIDEO IS AN EXAMPLE - here is a fun fact, but to investigate and understand it TAKES TIME and EFFORT.
The most likely effect is that you do not recall these ideas "Oh MrB is on another odd lesson that helps how, oh that was fun..." next lesson "Last lesson we did maths!" or "how does this help me pass my exams". Teachers I have seen and observed try to give this spark using these ideas, but the more often the students seem to take this.
THE BIGGER PROBLEM is the Societal acceptance that you "don't get" Maths, this is passed generation to generation; as a teacher parents saying "It's OK I didn;t get Maths id THE BIGGEST problem in teaching Maths".
This video leans into this attitude and I IMPLORE YOU to stop; my question is who and when did you discover these trinkets? How about the fun of how much is the loan I took for education, a car, my house going to cost me; compare it to how much I earn and its value, integrate the depreciation... the REAL WORLD... Nah! Its the future!... Maths teachers have real life skills that need to be communicated, but society dismisses them, thanks to denigrating the efforts of people.
**** This goes all such videos, cherry pick a surprising effect go for it - now integrate into a curriculum that has real application - MATHEMATICS is a LIFE LONG set of SKILLS in thinking, processing and decision making; and I AM ANNOYED MY HOW MEDIA REFLECT THEIR OWN ****IGNORANCE**** with such glib attitudes THESE ATTITUDES MUST CHANGE ****
This diatribe is not directed to BriTheMathGuy, but there is an Society Attitude that Mathematics is hard, and only the bright can master this THE ATTITUDE MUST CHANGE,.
(I would have made a video rebuttal - but I think my account would get blocked by the amount of swearing!!!!)
You…implore me?
Btw, which comment will have the most likes?
This one
@@VY_Canis_Majoris no man , already a comment having 17 likes
@@aashsyed1277 welp it was worth a try
You mispronounced mispronunciation.
Fun fact: Hₗₙ₍₆₎ is an incredibly good approximation of √2