Uploaded February 2023 | Updated September 2026, 2 weeks ago
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: Geometric magic square
30:59 Thanks!
The Korean historical drama Tree with deep roots is available here viki.com/tv/1585c-tree-with-deep-roots All the magic square action takes place in episodes 1 and 2.
Episode 1: the king's study with magic squares at 33:17 again at 42:00 (father "simplifies" magic squares)
Episode 2: lunchbox action starts around 46:00 then again at 58:39 (the AHA moment)
Lee Sallows's book: Geometric magic squares, Dover (2013)
His website: leesallows.com
His comprehensive online gallery of stunning geomagic squares: geomagicsquares.com
Nice write-up about the 33x33 magic square in Tree with deep roots: tinyurl.com/mszxrf2w
Wiki page on Claude Gaspar Bachet de Méziriac: en.wikipedia.org/wiki/Claude_Gaspar_Bachet_de_Méziriac
Eduard Lucas 3x3 magic square equation: en.wikipedia.org/wiki/Magic_square#Special_methods_of_construction
An app by Ilm Narayana that demonstrates the king's method for magic squares up to order 33 (thank you very much Ilm for accepting my coding challenge:) editor.p5js.org/ilmnarayana/full/KBhql96F9
Bachet's magic square algorithm write-up humanicus.medium.com/bachets-magic-square-c00c8ae4d56f (this article by Humanicus features the same proof that I present in this video)
Here is a magic square from an old Chinese manuscript en.wikipedia.org/wiki/Magic_square#/media/File:Suanfatongzong-790-790.jpg Among other things they are writing from top to bottom which would also have been done in Korea at the time. In fact, in the drama the tech support ladies can be seen writing from top to bottom. So that's a bit of a blooper when it comes to the writing on the tiles. A few other minor issues are discussed in the comments. What's also interesting here that they went for a 33x33 magic square and 33x33=1089. 1089 is a four-digit number and all the tiles are only labelled with three numerals. How did they write 1089 and still make sense? :) Why not use a 31x31 magic square? 31x31=961.
For the second method for building odd order magic squares check out this link: en.wikipedia.org/wiki/Magic_square#A_method_for_constructing_a_magic_square_of_odd_order
Some bugs:
- at 18:48, there is no green circle on the 2nd row 3rd column square.
- at 23:00, I should have said: take any 3 or more of the numbers that add to 15, then the corresponding pieces combine into the 4x4 with the bite (important because, for example, 7 and 8 don't work).
- at 28:20 one of the pentominoes is a hexomino :)
Today's music: Ardie Son - Counterparts
Today's t-shirt: 31415... Cannot remember where I found this t-shirt.
Enjoy!
Burkard
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: Geometric magic square
30:59 Thanks!
The Korean historical drama Tree with deep roots is available here viki.com/tv/1585c-tree-with-deep-roots All the magic square action takes place in episodes 1 and 2.
Episode 1: the king's study with magic squares at 33:17 again at 42:00 (father "simplifies" magic squares)
Episode 2: lunchbox action starts around 46:00 then again at 58:39 (the AHA moment)
Lee Sallows's book: Geometric magic squares, Dover (2013)
His website: leesallows.com
His comprehensive online gallery of stunning geomagic squares: geomagicsquares.com
Nice write-up about the 33x33 magic square in Tree with deep roots: tinyurl.com/mszxrf2w
Wiki page on Claude Gaspar Bachet de Méziriac: en.wikipedia.org/wiki/Claude_Gaspar_Bachet_de_Méziriac
Eduard Lucas 3x3 magic square equation: en.wikipedia.org/wiki/Magic_square#Special_methods_of_construction
An app by Ilm Narayana that demonstrates the king's method for magic squares up to order 33 (thank you very much Ilm for accepting my coding challenge:) editor.p5js.org/ilmnarayana/full/KBhql96F9
Bachet's magic square algorithm write-up humanicus.medium.com/bachets-magic-square-c00c8ae4d56f (this article by Humanicus features the same proof that I present in this video)
Here is a magic square from an old Chinese manuscript en.wikipedia.org/wiki/Magic_square#/media/File:Suanfatongzong-790-790.jpg Among other things they are writing from top to bottom which would also have been done in Korea at the time. In fact, in the drama the tech support ladies can be seen writing from top to bottom. So that's a bit of a blooper when it comes to the writing on the tiles. A few other minor issues are discussed in the comments. What's also interesting here that they went for a 33x33 magic square and 33x33=1089. 1089 is a four-digit number and all the tiles are only labelled with three numerals. How did they write 1089 and still make sense? :) Why not use a 31x31 magic square? 31x31=961.
For the second method for building odd order magic squares check out this link: en.wikipedia.org/wiki/Magic_square#A_method_for_constructing_a_magic_square_of_odd_order
Some bugs:
- at 18:48, there is no green circle on the 2nd row 3rd column square.
- at 23:00, I should have said: take any 3 or more of the numbers that add to 15, then the corresponding pieces combine into the 4x4 with the bite (important because, for example, 7 and 8 don't work).
- at 28:20 one of the pentominoes is a hexomino :)
Today's music: Ardie Son - Counterparts
Today's t-shirt: 31415... Cannot remember where I found this t-shirt.
Enjoy!
Burkard
