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Wednesday, February 15, 2012

B17: The Radian

Hello. This is my attempt at making the B17 (radian part of it) easier to memorize.
Hopefully this can help you as it has helped me.

Let's cut the circle in half and recapitulate:

Alright, so, we already know that the denominators go like this:

6, 4, 3, 2, 3, 4, 6. We also know that the numerators starting from the positive x-axis all the way to the 90° angle are always π. If you too have problems remembering what numerators come after the 90° angle, I think I have come up with a trick. I'll try my best to explain.

Hopefully you've noticed the pattern too.

Every time my teacher asks me to find the radians in the 2nd quadrant (as shown) counter-clockwise, I just say to myself: "2,3,3,4,5,6" and fill in the blanks.

But that's not all!

The pattern goes even further!
We've just added 7,6,5,4,4,3,3,2.

I find this long pattern easier to remember than the 17 radians, haha!


Notice that if we split this pattern like this:

2,3,3,4,5,6 (7) and

they're almost, what I like to call, "inversely-identical," except for the extra four.

Now, for the fourth quadrant, I have a different approach.

Actually, I've come up with a "temporary" formula to help you learn those tricky numbers:

n = 2d - 1

where "n" is numerator (of arms #14, 15, 16) and "d" is the denominator of either arms #1, 2, 3 or arms #14, 15 and 16.

This formula will automatically give you the coefficient of π!

Hopefully this will clear up your B17 problems. It sure did for me! :)

And if you still don't understand, or want to know another trick, here it is!

1 comment:

  1. Good heavens, you must have put a LOT of hours into this, Joey! Are you sure you want to be a police office, and not a math teacher? :) You seem to have a real love of explaining things....that's how I got hooked! Your system is brilliant, mathematically sound, and most importantly, it works for you. I am sure it will help others, not to mention inspire others to come up with their own system AND share it as well. In colour. On their blog. Thanks again!