We have looked at squares and the significance they play in the philosophic speculation on numbers. One of the principle ways of understanding numbers is in their relationship to one another. For example, through the means of ratio the search for the ideal size of the unit, 1, the Monad, revealed the unique and important roles of 8 and 9. (See Ratios)
When we consider the square of 17 we find it yields 289.
But 289 is one more than 288, which is twice the square of 12 (144 x 2). 12 we recognise as the Solar number of the Year. There are 12 signs in a solar year. This is not exactly accidental. The number 360 was chosen as the number of degrees in a circle because that is the number of days – approximately – that it takes for the Sun to return to its position in the Heavens. This leads to the use today of 30 degrees as a significant degree. So we find that four of the months of the year are 30 days in length. 12 x 30 = 360. One full circle, or (almost) one full year.
So that’s something about 12 and why we use it today.
But we also need to notice that 17 squared is slightly more than the square of 12 doubled – doubled because these are the two sides of right-angled triangle, or a square. The diagonal of such a square is then shown to be just short of 17.
But there is a better equality than this. It consists of the square of 15 added to the square of 8. 8 x 8= 64; 15 x 15 = 225. 225 + 64 = 289. A much better fit than simply 2 twelves.
So these are some of the significant features of the number 17.
But we began this talking about the importance of ratios and the place of 8 and 9 in relationship.
When we consider 8 squared and take it from 9 squared we find the interval between them is 17. 81-64 = 17.
So what? It had to be somewhere! But this is the reinforcing nature of numbers. When one is discovered to have a particular relationship to another and then to have that relationship – or relativity if you prefer – strengthened indicates a particular bond between them. This explains the excitement that Pythagoras felt on the discovery of the 3, 4, 5 triangle. Though many claim it was not he who first discovered this. But then most people think of numbers only in terms of how many have they got of whatever it is they suppose they possess.