Alright, party people. The last few weeks of introducing the Vedic 9 point circle have been fun, but I’ve been dying to get to the point where I can show you what you can really start to do with it…and today is the day!
So, I thought the 9 point circle had a limited amount of fun until I started studying a vedic illustration that looked like this:
which looked more artsy and less mathsy. And, well, that’s the point. Art, math, philosophy..it’s all the same. In fact, the basis for this type of math is centered on 16 vedas, or sutras. For a very in depth discussion of these guiding principles, visit here and kind of skim down until you get to the ‘Nature of the Sutras’ section. I haven’t delved deeply into the sutras at this point, either for Math Mondays or in my own studies, because honestly we are having so much stinkin’ fun with the 9 point circle still. We haven’t moved on yet!
So, gather around you everyone who claims to hate math (yourself included!), and arm yourself with a 9 point circle.
The first thing you need is someone who loves math. I know, they can be obnoxious and spoil the “I hate math” fun, but you need someone to do the multiplication tables for you. Luckily, Naturalist and I have Golfer nearby. If you don’t have someone like this available, use a calculator. The point of this exercise isn’t to see how good you are at memorizing multiplication tables (I still haven’t done it!) but to find these super cool patterns in the circle. So–don’t get bogged down in the numbers. Free your mind to do other things like draw lines in pretty colors!
The second thing you need is to start writing down the multiplication tables. The designated math lover will love this. Then, the designated math hater can start taking those numbers and ‘graphing’ them on the circle. For instance, start with 1. Multiplying in order, the numbers (multiples) will be 1,2,3,4,5,6,7,8,9,10,11, etc. When you graph them on the circle, it looks like this:
You may have realized that 10, 11, etc., are all two digits and ungraphable on the chart. Good for you! This is why I talked about digit sums last week. If a number is more than one digit, add the digits together until it becomes a number between 1 and 9. Then graph it. You may have realized that the multiples of one have a cool pattern on the circle…they are an endless loop. 1-9, 1-9, 1-9 repeating forever, no matter how big the numbers get…the digit sums repeat the pattern.
Now look what 2 does:
!!! It is also on a repeating loop. Can you work it out? Have the designated math lover show you the multiples of two, and then when you and the other math haterz graph it, you can appreciate it’s pattern.
But just wait until 3. You won’t believe it. You will be amazed and overjoyed. Because math haterz may not like numbers, but we all love a good picture…a nice shape. And when we realize that numbers can make lovely shapes, all of a sudden the numbers that we may hate so much begin to hold a certain appeal. So…I bring you….3…
Can you STAND it?! Didn’t your mind look at that and think, “I’ve got to multiply 3 over and over to find out how this triangle is possible!” Ours did. In fact, Golfer wasn’t done with some other computations, so Naturalist and I were doing the 3′s ourselves and almost fainted when we saw the pattern on paper, with the numbers…and we hadn’t even graphed it yet.
We stopped here for the day, when we explored it. So, for the first time in my life I spent that night thinking of numbers. What patterns would the multiples of 4 make? 5? 6?
We’ve made number patterns like this for the past couple weeks. Each day uncovering a couple new shapes, and each night leaving me to ponder the shapes that numbers make. I even started figuring out multiples of 15, people! Me! The biggest math hater around town. But we discovered the triangle shape in number 3, then 6, then 12, and I had to know if it continued the pattern for 15. (A pattern in a pattern!) See…
And if the pattern holds for multiples of 3, why wasn’t 9 a triangle? And, what pattern was 9 if it wasn’t a triangle? I almost hate to show this right away…maybe I should just leave the questions hanging there for you to discover the answer yourself. But I can’t. I’m horrible at keeping cool things to myself. So I’ll just share 9:
And next thing you know, we’re wondering if multiples of 3 seem to be triangles, are multiples of 9 just a dot? So Naturalist and I started figuring out multiples of 18, 27, 36, etc. Sometimes mentally if the calculator was busy. And, well, I’ll just let you do the graphing for those–I’ve spoiled the surprise on to many numbers already.
There is an entire wall of our breakfast nook devoted to our colorful little drawings:
I must admit, this is the first time I’ve looked forward to doing math. Naturalist, too! And maybe…you, too!