Math Monday:: More Number Circles!

In Vedic Math, there isn’t just a ten point circle, there’s also a 9 point circle as well. And, you all know how much we love circles around here! Circular logic, circular thinking, circular donut, whatever. If it’s a circle, it’s good.

The 9 point circle is tons of fun, especially to someone who has learned to hate math/numbers. There isn’t anything very fun about a bunch of numbers in a long line, but wait till I tell you about what happens when you wind those boring numbers up into a circle, like this:

Vedic 9 Point Circle

Play along, if you’d like. First, take a circle and put 9 lines like spokes on it. 9 is up top, then going from 1, label the lines until you get back to 9 again. Then, keep going with the 10 placed alongside the 1, 11 alongside the 2, 12 alongside the 3, etc. Do this for as long as you have room, or until you want to stop. This is when it starts getting fun.

Pick a spoke, any spoke. Let’s say, spoke 4. Now look at all the numbers coming off from that spoke: 4, 13, 22, 31, 40, 49, … There’s something interesting about them. They go up by 9, yes. But they do something else, too. Golfer, who is our math whiz, couldn’t see anything else. Naturalist, who is our mathphobe, got it in an instant. It’s all about the patterns! “The numbers all add up to 4! 13…1+3 is 4! They all do that!” And they do.

She was excited at this point, and wanted to see if the pattern held true for every spoke…which it does. In fact, you can place any number out of order on the correct spoke by figuring out the digit sum (numbers added together until there’s only one digit) and putting it on that spoke.

Well, I’m happy to say that the mathphobe, who is good at avoiding adding numbers at all costs, wanted to take big long numbers and keep adding the digit sum until she could put it on a spoke. We started with birthdays. She is 8/17/1996. So, her digit sum would go like this:













You might notice we took some extra steps, dividing up the larger teen numbers–it’s because neither of us like to add big numbers like that, so we just broke them up first, and continued on.

Eventually we discovered things, like–a 0 doesn’t move you around the circle, so you can ignore those. A 9 moves you around the circle, but keeps you on the same spoke, so you can ignore those. Golfer had the best birthday to show that: 8/19/1999. The long way to get the digit sum is like this:









(note: Golfer adds big numbers better than we do, so it’s a bit quicker for him)

But we can “cast out the nines”, meaning, ignore them since they keep us on the same spoke anyway, so his number becomes:


Just like that! He didn’t have to add anything!

We spent an afternoon adding digit sums–it became obsessive, especially when we realized we could get rid of the 9’s to shorten our number. My birthday was kinda fun, but not like Golfers: 11/12/1972 (now you know how old I am…all in the name of math…)

I cast out the 9, as well as the 7 and 2 because those make 9, so my number became 11/12/1…




We looked to see if anyone shared a spoke with anyone else. I’ll tell you what, for two girls who hate to add, Naturalist and I couldn’t stop doing this. It makes for a fun little game.

Go ahead…try it!

Some videos in case I was confusing up there:

9 Point Circle:

Digit sum and casting out the 9’s”