Also notable are the ancient cultures with a tradition of mathematics and numerology that did not discover the magic squares: Greeks, Babylonians, Egyptians, and Pre-Columbian Americans.
While ancient references to the pattern of even and odd numbers in the 3×3 magic square appears in the I Ching, the first unequivocal instance of this magic square appears in a 1st-century book Da Dai Liji (Record of Rites by the Elder Dai).
These numbers also occur in a possibly earlier mathematical text called Shushu jiyi (Memoir on Some Traditions of Mathematical Art), said to be written in 190 BCE.
This is the earliest appearance of a magic square on record; and it was mainly used for divination and astrology.
That’s going to be my 50s, this is going to be my 60s, 70s, 80s, and then I have my 90s right over here. I’m almost done filling in my numbers from zero to 99.
And so this one we already said this is going to be my 40s, this is going to be my 50s, this is going to be, I’m trying to make sure I use all my colors, my 60s, this is going to be my 70s, and then I have my 80s, and then of course I have my, let me do a color that, I’ll re-use magenta, I’ll have my 90s. Now I can do it over here, 42, 52, 62, 72, 82, and 92. 49, 59,69,79,89,99 and if we just wanna feel good, we could throw in, we could throw in a 100, a 100 right over there.In India, all the fourth-order pandiagonal magic squares were enumerated by Narayana in 1356.Magic squares were made known to Europe through translation of Arabic sources as occult objects during the Renaissance, and the general theory had to be re-discovered independent of prior developments in China, India, and Middle East.The 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 = 4k (e.g.4, 8, 12, and so on), oddly even (also known as "singly even") if n = 4k 2 (e.g. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares.So let me just start, so I’m gonna start at zero, one, two, three, four, five, six, seven. Well it’s a 12, which is a one followed by a two, and then 13, 14, 15, 16, 17, 18, and 19. This next row of numbers as I went from 10 to 19 looked just like the first ones, so the 2nd number is the same in yellow, but then I added a purple one to the front of it. So just doing that I think you already see the pattern.eight, and nine, and instead of, of course we know the next number is 10, which I could write down but instead of doing that I’m just going to copy and paste all of this. And one way to think about it is, each of these numbers, the purple one that I added, that represents 10. So let’s take another row , my original row, and what do I get to after 19? So 20, two zero and then 21, 22, 23, 24, 25, 26, 27, 28, 29. The number on the right we keep going from zero, one, two, three, four, five, six, seven, eight, nine, and then the number on the left, if we’re between 10 and 19, you’ll always have a one.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.Now how can I complete this going all the way to 99 pretty fast?Well let’s do that, so that’s going to be my 40s, I haven’t written it out yet.