Voiceover: The goal of this video is to essentially write down all the numbers in order from zero to a 100.But I’m going to do it in an interesting way, a way that maybe will allow us to see some patterns in the numbers themselves. So the first number 30 is 30 plus zero, 30 plus one, 30 plus two, 30 plus three which is 33, 34, 35, 36, 37, 38, 39.
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.
So what if I woulda just take this, so let me just take this right over here, and copy and paste that. And I can do it for each of these, for each of these now. And you’ll see the pattern still holds, we went from one, two, three, four, five, six, seven, eight, nine, and now we got to 10 followed by a zero.
The mathematical study of magic squares typically deals with its construction, classification, and enumeration.
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.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.In regard to magic sum, the problem of magic squares only requires the sum of each row, column and diagonal to be equal, it does not require the sum to be a particular value.Thus, although magic squares may contain negative integers, they are just variations by adding or multiplying a negative number to every positive integer in the original square..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.By the end of 12th century, the general methods for constructing magic squares were well established.Around this time, some of these squares were increasingly used in conjunction with magic letters, as in Shams Al-ma'arif, for occult purposes.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).