Category Archives: Sweet Math

On essentials.

Hey kiddo, I see you’ve brought your calculator to breakfast. Are you planning to do some computation while you eat?

[Fixes me with a cold, fishy stare.]

Yyyyyyyyupppp.

On math. Delicious math.

[We have been talking a lot about the speed of light, which is a constant value.]

Are there other mathematical constants?

Yes. There’s a cool one called pi that helps us figure out the circumference and area of any circle. Would you like to do some work with it sometime?

YES YES BRING ME THE CONSTANT PIE!

[Later]

Pi is also cool because it goes on forever. You can’t write it as a simple fraction – its decimals go on forever if you don’t round it – which, clearly, you have to at a certain point. That’s called an irrational number.

CONSTANT ENDLESS PIE! YUMMMMMMMM

On Pythagoras and Einstein.

[We are reading Why Does E=MC2? (And Why Should We Care) by Brian Cox and Jeff Forshaw aloud. I have just got to a tricky bit about how time is not absolute – that time slows down the faster you go, illustrated by an example of light bouncing between mirrors in a light clock on a train. The example includes a fun little bit with right angle triangles and some work with D=Speed x Time, which is all new to Allie.]

Ok, so before I read this next bit through, I want to grab a pencil and mark up some diagrams so you can see what’s happening. Here we have a light clock, as we would see it if we were passengers sitting next to it on a train. The light beam goes up, hits the first mirror, and comes straight back down and hits the other one – boing, boing. We’ll count that as one tick. 

Yes, yes. I’ve got it.

And then over here we’re going to look at the same light clock, but from outside the train, standing on the platform as the train moves along. We see the beam go up like it did before, but the train is moving to the left, so it doesn’t go straight across, it makes – 

That long angle. Yes, yes. The train is moving so the beam hits over there and then down there. [Points to diagram]

Right. So then we can use some fun geometry to figure out how much time that beam takes to go on that big angle. For that, we’ll use the Pythagorean Theorem which is an awesome way to find out the length of the long side of a Right Triangle. [Pause for a bunch of math/ scribble, scribble.] Does that make sense?

Yes. Yes. YES. Of COURSE that makes sense. So we get two different answers for the length of the tick in the two different situations. There is no such thing as absolute time! CAN WE READ THE ACTUAL BOOK NOW?!