Unsolved problems in mathematics | Magic squares | Matrices
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The order of the magic square is the number of integers along one side (n), and the constant sum is called the magic constant. If the array includes just the positive integers , the magic square is said to be normal. Some authors take magic square to mean normal magic square. Magic squares that include repeated entries do not fall under this definition and are referred to as trivial. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant we have semimagic squares (sometimes called orthomagic squares). The mathematical study of magic squares typically deals with their construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Magic squares are generally classified according to their order n as: odd if n is odd, evenly even (also referred to as "doubly even") if n is a multiple of 4, oddly even (also known as "singly even") if n is any other even number. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century. Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations. (Wikipedia).
Magic Squares part 3: The magic in the mirror.
Time to start to learn how to build even-order magic squares! Playlist:https://youtube.com/playlist?list=PLV_8Ld73yCWEJlCA4LQrioGYgMCn4gN7x Part 1: https://youtu.be/dvkREHaqQWM Part 2: https://youtu.be/-r2VPdxjCqE Part 3: https://youtu.be/seCFxxnid_0 Part 4: https://youtu.be/2h3DHubiROo
From playlist Magic Squares
Bit of Da Vinci Code moment here as Professor Eaves fuses his love of mathematical games and a famous piece of art. More videos at http://www.sixtysymbols.com/
From playlist Magic Squares on Numberphile
Magic Squares part 4: The most magical of them all
This is the last part. Enjoy my very special magic square! Playlist:https://youtube.com/playlist?list=PLV_8Ld73yCWEJlCA4LQrioGYgMCn4gN7x Part 1: https://youtu.be/dvkREHaqQWM Part 2: https://youtu.be/-r2VPdxjCqE Part 3: https://youtu.be/seCFxxnid_0 Part 4: https://youtu.be/2h3DHubiROo 00
From playlist Magic Squares
How to make a Birthday Magic Square
A birthday magic square is a special type of magic square that uses someone's birth date in the top row. Then every row, column, and main diagonal add up to the special birthday number - and a whole lot of other magic properties as well! ----- Notes: Some people have realised it isn't al
From playlist My Maths Videos
SOLVE The 3x3 Magic Square Completely - There Can Only Be One!
A magic square has every row, column, and diagonal sum to the same number. How many magic squares are there using the numbers 1 to 9? This video shows you all the possibilities and proves there are no others, leading to the surprising result the 3x3 magic square is essentially unique, up
From playlist Magic Tricks
What kind of magic is this?! #shorts #math #maths #mathematics Sia - Chandelier https://youtu.be/2vjPBrBU-TM
From playlist Math Shorts
The torus magic is constructed with many rings. It transforms flat,spherical,etc. Farther more you can turn it inside out.
From playlist Handmade geometric toys
ʕ•ᴥ•ʔ Unit Circle and Reference Angle Trigonometry Explained
Quickly master unit circle and reference angle Trigonometry. Watch more lessons like this and try our practice at https://www.studypug.com/algebra-2/trigonometry/unit-circle What is a unit circle? Unit circle is nothing crazy. It's just a circle with radius equal one. Unit circle just me
From playlist Trigonometry
A double feature on magic squares featuring Bachet's algorithm embedded in the Korean historical drama series Tree with deep roots and the Lee Sallow's geomagic squares. 00:00 Intro 02:52 Part 1: The king's magic squares 09:40 Proof 18:22 The order 5 and 7 magic squares 19:17 Part 2: Geom
From playlist Recent videos
Follow-up: Birthday Magic Square
This is my follow-up video to my birthday magic squares video https://youtu.be/hNn0j4Kay8g --- Yeah, I know the audio is messed up. It's not the mic, it's because I recorded via OBS, and that messed up the audio. Sometimes it's difficult to get all the tech working. I tried. If the audio
From playlist My Maths Videos
Make A 9x9 Magic Square! Learn The Ancient Chinese Algorithm (Lo Shu Square)
Magic squares are arrangements of numbers where every row, column, and diagonal adds up to the same number. The ancient Chinese developed a geometric method to create 3x3 magic squares. Remarkably, they generalized the method to create a 9x9 magic square which is quite the feat! The Lo Sh
From playlist Magic Tricks
Magic Squares part 2: The odd 5×5 can make you win a bet.
Making the panmagic square with any number as the magic constant is a little tricky but the result is worth it. Playlist:https://youtube.com/playlist?list=PLV_8Ld73yCWEJlCA4LQrioGYgMCn4gN7x Part 1: https://youtu.be/dvkREHaqQWM Part 2: https://youtu.be/-r2VPdxjCqE Part 3: https://youtu.be
From playlist Magic Squares
Magic Squares part 1: the secrets of the 3×3
Tell me if you learned something new! First of my series about magic squares. Enjoy! Playlist: https://youtube.com/playlist?list=PLV_8Ld73yCWEJlCA4LQrioGYgMCn4gN7x Part 1: https://youtu.be/dvkREHaqQWM Part 2: https://youtu.be/-r2VPdxjCqE Part 3: https://youtu.be/seCFxxnid_0 Part 4: https
From playlist Magic Squares
Dr James Grime talking Magic Hexagons (and magic squares). More links & stuff in full description below ↓↓↓ Support us on Patreon and get extra stuff: http://www.patreon.com/numberphile James Grime: http://singingbanana.com Support us on Patreon: http://www.patreon.com/numberphile NUMB
From playlist James Grime on Numberphile
Squaring the circle illusion #shorts
How to make a shape that looks like a square from one direction and a circle from another. Buy from Shapeways: http://shpws.me/Te9N Download to print yourself: https://www.printables.com/model/270848-squaring-the-circle-illusion
From playlist 3D printing
3.1 Million Views. The Return Of The (Sudoku) King
You can try Aad van de Wetering's latest masterpiece here: https://cracking-the-cryptic.web.app/sudoku/nLfTB6T9t8 Rules: Normal sudoku rules apply. Both main diagonals (marked) contain only ODD digits. The two marked grey squares in the grid (upper left and bottom right) are magic squa
From playlist Aad Van De Wetering Puzzles