From Vsauce2. The Knight’s Tour is a game that starts easily and becomes impossible. The idea is to make a grid of squares starting with a 3×3 arrangement and move your ‘Knight’ through the grid without crossing its own path. Whether your goal is to touch as many squares as possible, make the most efficient…

From Vsauce2. Graph theory is a discipline that seems to get more important every day. It maps relationships between objects, and that has lots of practical uses. Graph theory is what determines your postal delivery worker’s most efficient route through a series of neighborhoods. It’s what tracks the spread of public health crises and undergirds…

From Vsauce2. With just 8 matches (or pens or q-tips or anything straight), you can tie up your mind for hours, days, or WEEKS. The idea is to develop a basic understanding of graph theory, which focuses on the relationships between things — and you can express those relationships visually. Each match consists of three…

From Vsauce2. A tremendous amount of math is found in nature, and it’s most obvious in Fibonacci/Golden Ratio patterns in the world’s flora. But the Schumanniophyton problematicum plant’s leaves are determined by algebra, and a simple equation can tell you exactly how many leaves it has or how long it’s lived. The Schumanniophyton problematicum’s leaves…

From Vsauce2. The best way to divide a certain class of numbers is to use absolutely no math at all. WHAT?! It’s true — you can get the job done simply by transposing the first digit to the end of the number. 410,256 is a small, accessible number to try it. Just slide the 4…

From Vsauce2. This simple geometrical game requires you to divide equally and conquer, and it hearkens back to the most popular math game in the history of the world: Tetris, but in reverse. The object here is to come up with every possible way to divide a square grid into two perfectly symmetrical parts. Once…

From Vsauce2. Some recreational mathematicians call this sort of thing a "Digital Bracelet" because it’s a circular arrangement of digits that has no clear beginning, end, or even direction. The digits 1, 9, 3, 9, 3, 9 can be progressively transposed to create a fluid circle of 6-digit prime numbers that works forward and backward.…

From Vsauce2. If we count 1 as a prime digit, you can start with 1, 2, 3, 5, or 7 and build Snowball Primes — prime numbers that remain prime each time you add another digit. Start with 3? Add a 1, still prime. Start with 7? Add a 3, still prime. 73, add a…

From Vsauce2. There’s not much to simple combinations with no replacement… if we take the 10 digits from 0 to 9, we can arrange them nearly 4 MILLION ways by using 10!. When we take the subset of squared digits that result in a unique combination of those 10 digits? Now we’re down to just…

From Vsauce2. Strobogrammatic numbers go beyond quantity to harness rotational symmetry — they have visual meaning, too. Numbers that use 6 and 9 are the most obvious examples, since flipping them upside down retains their full quantity and meaning… 69 is exactly the same right-side up or turned 180 degrees. And why does it matter?…

From Vsauce2. Magic squares are pretty amazing, but they’re simple in the sense that the Magic Constant is constructed from the same quantity of spaces in every direction — vertical, horizontal, and diagonal. A Magic Honeycomb? It can’t have vertical paths to the constant because the spaces just don’t connect that way… but there’s an…

From Vsauce2. Go to https://noom.com/vsauce2 and take your free 30-second quiz! Thanks to noom for sponsoring Vsauce2. The criminal justice system is overburdened and expensive. What if we could harness advances in social science and math to predict which criminals are most likely to re-offend? What if we had a better way to sentence criminals…

From Vsauce2. Some people call the Golden Ratio ‘the most beautiful number in the universe.’ We have uncountable examples of the Golden Ratio appearing in nature and the world around us, but just because it’s a number doesn’t mean it can’t sneak into the alphabet, too. Breaking down the symmetrical pairs embedded in the Latin…

From Vsauce2. There are only a handful of truly legendary numbers, like 0, 1, and Euler’s Number. And there are only 10 digits from 0-9, so it would make sense that we can shift them around to see some interesting things… right? Sometimes it feels like too much of a coincidence, like being able to…

From Vsauce2. One of the most interesting puzzles in recreational mathematics is the construction of a Magic Square, an arrangement of numbers in which every single row, column, and main diagonal add to the exact same number. The classic introductory magic square is of Order 3, meaning there are 9 total spots in a 3×3…

From Vsauce2. It’s taken thousands of years for humans to decide what zero is, and also what zero isn’t. It’s a strange concept to think about what nothing really means in relation to other numbers, but giving zero meaning beyond a simple placeholder was one of the most important advances in mathematics. Indian mathematician and…

From Vsauce2. Get Surfshark VPN at https://surfshark.deals/vsauce2 and enter promo code Vsauce2 for 83% off and 3 extra months for FREE! Documentaries, television and movies are obsessed with crime. Is the accused actually guilty? If not, who is? If so, will they get away with it? All these questions matter — but the most important…

From Vsauce2. How many times have you heard that the shortest distance between two points is a straight line? What if it’s actually… the longest distance? What if it’s an infinite distance? What if it’s impossible to move at all?! That’s the theory behind Zeno’s thought experiment on movement. If every distance can be divided…

From Vsauce2. Blaise Pascal’s Triangle displays the array of binomial coefficients in a triangle that holds a different meaning from seemingly every angle. From the odd numbers creating a fractal similar to the Sierpinski triangle to generating a full Fibonacci Sequence, Pascal’s triangle portrays mathematical beauty — and also keeps track of coin flips. Buried…

From Vsauce2. As borders twist and turn through geographic features and political realities, maps get complex quickly. But no matter how many bodies are being mapped, it’s only necessary to use 4 different colors to make sure that no two that are touching share the same color. Given how intricate and complicated maps can be,…

From Vsauce2. The world’s smallest skyscraper wasn’t supposed to be that way… depending on who you ask. When the Newby–McMahon Building in Wichita Falls, Texas was completed in 1919, investors were shocked. They’d put the equivalent of $3 million today into what was meant to be a 480-foot building. Instead, they got a 480-inch building,…

From Vsauce2. Blaise Pascal may have published Traité du triangle arithmétique in 1665, but the world knew about his triangle centuries before. Scholars in India, Persia, China, and even Germany played with the possibilities of a pattern of binomial coefficients, but Pascal brought it to the broader world. Pascal’s Triangle is easy to construct by…

From Vsauce2. Police lineups are notoriously difficult to get right, and a huge part of that is your brain’s fault. When you’re presented with a lineup that shows someone similar, but not the same, as the suspect, your brain tends to fill in the gaps. It basically selects the next best option to the truth,…

From Vsauce2. Jennifer Thompson was the perfect witness. She was smart, perceptive, and alert during her attack. She made a conscious effort to note every little detail to help police identify the man who assaulted her. She identified him with 100% confidence in a photo lineup, then during an in-person lineup, and again at the…

From Vsauce2. The 24 game that originated in China is a fast-paced 2-player game of number manipulatiin. Your goal is to take the integers of the 4 cards on the table and turn them into the number 24, and any mathematical operation is fair game. Add, subtract, divide, multiply, fractions, exponents, factorials… anything goes, as…

From Vsauce2. Narcissistic numbers are numbers whose individual digits raised to the power of the total number of digits can be added together to create the original number. So, for 153, that means 1^3 + 5^3 + 3^3 = 153. How big can they get? And do they even matter? No… and yes. GH Hardy…

From Vsauce2. Pi is hidden everywhere, including inside a sequential alphabet clock. WHAT?! If you make a circle of the 26-letter Latin alphabet from A to Z, and then erase every single letter with vertical symmetry (like cutting down the middle of W or T so the left and right sides are mirror images), you’re…

From Vsauce2. You all know the Pythagorean theorem, but what does a right triangle with a hypotenuse of 684,912,110,217,988,900 reveal about Pi? A lot, once you figure out the other two sides. If the square root of 684,912,110,217,988,900 yields 827,594,170, and that equals a^2 + b^2, we can find the ratio of a to b.…

From Vsauce2. By starting with the prime number 71, you can make a simple recipe for pie. If 71 is the denominator, a numerator of 208 yields two important mathematical constants with +/- 15. 223/71 gives you a very close pi approximation, and 193/71 is just thousandths away from Euler’s number. Put them together and…

From Vsauce2. You can determine the number of trailing zeroes on a factorial of ANY size with a pretty simple trick that involves dividing by powers of 5. First, you can do it the hard way, and multiple every number of x! (x * (x – 1) * (x – 2)…) until you’re multiplying by…

From Vsauce2. A megaprime number is a prime with at least 1,000,000 digits. Not only is there an infinite number of megaprimes, but it means that almost every prime number is a megaprime. But why stop at a million digits? A gigaprime or bevaprime is a prime number with at least a BILLION digits —…

From Vsauce2. Every number is unique, but not every number has special properties. Actually, most of them don’t have interesting characteristics… half of all numbers are even and divisible by 2, so they can’t even be prime. 0 and 1 are in a class by themselves, but 11 is actually pretty distinctive. It’s prime, it’s…

From Vsauce2. You can take any number with 2 or more digits and determine almost instantly whether it’s divisible by 11, and the method is actually really, really easy — even for a number like 2,399,317,565,387,204. All it takes is simple addition and alternating between the odd and even digits. If the difference between the…

From Vsauce2. Start speaking a new language in 3 weeks with Babbel. Get up to 65% OFF your subscription: https://go.babbel.com/12m65-youtube-vsauce-feb-2022/default Thanks to Babbel for supporting Vsauce2. Kristen Gilbert was nicknamed the “Angel of Death” because so many patients happened to die during her shifts. No one saw her doing anything wrong, and there just wasn’t…

From Vsauce2. You can write the numbers 1 through 10 using ONLY the digits 1 and 9… and eventually it gets a little complicated if you try not to repeat any terms. You can use any signs or notation, but you’re limited to just 1 and 9 on the numbers. So, 11 = 9 +…

From Vsauce2. Indian recreational math genius D.R. Kaprekar has a set of numbers named after him, and a Kaprekar number occurs when you square that number, then add up the resulting digits to the original number. So, 55 is Kaprekar because squaring it gives you 3,025, and 30 + 25 = 55. You’d think that…

From Vsauce2. Some numbers are happy. Some numbers are sad. How can you tell the difference?! It’s actually really easy. Square the number, then square the resulting digits and add them together. Do it again and again… if you get to 1, that number is happy. And if you can’t get to 1, the number…

From Vsauce2. Start building your ideal daily routine. The first 100 people who click on the link will get 25% OFF Fabulous Premium: https://thefab.co/vsauce2 Thanks to Fabulous for supporting Vsauce2. Numbers don’t exist in a vacuum, especially when they make up a game that’s an essential part of a community. And sometimes they turn into…

From Vsauce2. A handful of numbers have a very special property: you can add their digits together and divide the original number by their total without a remainder. And why does it matter? Well, in terms of mathematics, it’s mostly a curiosity. Dattatreya Ramchandra (D. R.) Kaprekar saw these numbers as sparking joy in the…

From Vsauce2. We can’t write out every digit of Pi every time we use it, but we’ve got to represent it somehow. And you were probably taught that 22/7 was a great option. Well… it’s an okay option. It’s not bad, but it’s not amazing. 355/113 is so close to the real value of Pi…

From Vsauce2. Usually when you look at a nice round or coordinated number, it’s components are obvious. Like 333 — you know there are 111 threes in there, and even 111 is made up of 37 threes. 1,000 is 10 hundreds, and those hundreds are 10 10’s. But when you break down 1,111,111, you find…

From Vsauce2. Bitdefender Total Security (Extended Free Trial) – https://www.bitdefender.com/media/html/consumer/new/WI-S-Bitdefender/?cid=inf&7Cc%7Cig¾7CVS2Q4 Thanks to Bitdefender for supporting Vsauce2. We know what infinity is… it’s something that never ends. It’s right in the name: ‘doesn’t finish.’ But is it possible to have more than one infinity? Can one infinity be larger than another? And if we say yes…

From Vsauce2. Bitdefender Total Security (Extended Free Trial) – https://www.bitdefender.com/media/html/consumer/new/WI-S-Bitdefender/?cid=inf%7Cc%7Cyt%7CVS204 Thanks to Bitdefender for supporting Vsauce2. As math and our minds both become more sophisticated, we can use strategies like probability to fill gaps in the unknown. That’s particularly useful in a court of law, where we almost never have all the facts we need.…

From Vsauce2. Goldbach’s Conjecture states that every even whole number greater than 2 is the sum of two prime numbers. So, 28 is 11 + 17… 62 is 43 + 19… and it goes up. WAY up. We’ve calculated every value up to 4 x 10^18, so it’s got to be provable, right? WRONG. One…

From Vsauce2. Sign up to Morning Brew for free today: https://bit.ly/mbvsauce2 Thanks to Morning Brew for supporting Vsauce2. “… for the root of all evils is the love of money,” states the First Epistle of Paul to Timothy — and no woman in 19th century America exemplifies that more than Hetty Green. She was a…

From Vsauce2. Just because you see a number like 100,000 doesn’t mean it’s actually 100,000. We operate in a base-10 numeral system, and it’s got the familiar 10-based decimal root — and "decimal" even comes from the Greek "deca" prefix meaning 10. But… not everyone thinks of the world in tens. Mainland Europeans used dozens,…

From Vsauce2. Where would we be with this dot?! It doesn’t seem like much, but it’s a critical element to our quick understanding of numbers. Without a decimal point or radix point, we have to mentally solve a little puzzle to figure out what the numbers we see actually mean. But with it, we know…

From Vsauce2. What do you do when you’ve got a mathematical expression that’s unsolvable because the numbers you need don’t exist? You do what Hero of Alexandria did: you just invent one. That’s how we got the concept of imaginary numbers, which Rene Descartes derided as being totally useless. Turns out he was wrong. #shorts

From Vsauce2. Go to https://keeps.com/Vsauce2 to get 50% off your first order of Keeps hair loss treatment. Thanks to Keeps for sponsoring this video. When Joyce Ann Brown saw her name in the newspaper in connection with a gruesome murder, she went straight to the police to clear up the obvious error. She was at…

From Vsauce2. Find out which companies have your data and reclaim it by visiting: https://bit.ly/saymine-vsauce2 Thanks to Mine for supporting Vsauce2. When tragedy struck Madrid on March 11, 2004, the international community including the FBI rushed to help Spanish police identify the perpetrators. Some of them were too eager. A partial fingerprint match to Oregon…

From Vsauce2. What IS 1? It seems like a really stupid, obvious question, but the truth is that 1 is seriously complex. Is it even a number? Number theory pushes and pulls on 1, showing that it’s everything all at once — yet sometimes it’s powerless. Cube it, multiply, divide it… whatever you do, it’s…

From Vsauce2. There are infinite ways to write the number 1 without even using a 1. But what’s the simplest way to write 1 using all 10 digits 0 to 9? You can do it with exponents, square roots, multiplication and division… really, anything goes. But the easiest, least-complicated way to get all 10 digits…

From Vsauce2. Of all the numbers, why is THIS one so weird? Multiply it and you’ll get the same re-arranged digits, or leave it on its own — which happens to coincide with the repeating value of 1/7… It shouldn’t be like this. Why is this happening? WHY IS 142,857 SO SPECIAL? #vsauce #education #math

From Vsauce2. Was "alogon" unsayable because it was a mathematical Voldemort, or because the concept of irrationality was so difficult to express? Probably a little bit of both. Hippasus’s fate is a mix of legends, with some saying he was drowned at sea by the will of the Gods after discovering irrationality, and others suggesting…

From Vsauce2. Think about how people discovered fractions and what problem they were meant to solve. How do we take a thing and express its division into smaller equal parts? A lot of little somethings add up to 1… until 2/3 came along. Using a numerator that isn’t 1 doesn’t sound like much, but it…

From Vsauce2. The Egyptians didn’t know the Pythagorean Theorem, but they figured out a way to make perfect 3-4-5 right triangles using segments of rope. It’s so common sense, unsophisticated, and elegant that it’s an example of a proof without words AND mathematical beauty. #shorts

From Vsauce2. Just think of all the questions that arise when a seemingly-healthy baby dies. Was there an illness that went undetected? Was there a rare genetic defect that couldn’t possibly have been known? Are any signs of physical trauma related to the resuscitation efforts of a fragile infant, or something more sinister? Every time…

From Vsauce2. Nicomachus wrote "Introduction to Arithmetic" nearly 2,000 years ago, but he also seems to have come up with the first mathematically-based mind blows in Syria. Given the average person’s understanding of mathematics at that time, who WOULDN’T think Nicomachus was a wizard? #shorts

From Vsauce2. Get the Vsauce Curiosity Box: https://www.curiositybox.com/vsauce2 Probability is one of the clearest, more straightforward disciplines within mathematics. Unfortunately, almost nothing in mathematics is murkier and more misleading than… probability. WHAT?! Belgian mathematician Maurice Kraitchik posed a simple question about wagering wallets, and in doing so he revealed a paradoxical mismatch between a raw,…

From Vsauce2. What happens when you take a number, reverse it and add them together? Over and over and over? Something quite SYMMETRICAL emerges. Except for 196… and no one knows why. #shorts