It’s funny that sometimes the most straightforward ideas can sometimes be quite surprising (for me anyway) The latest such idea is that the circumference of a circle with diameter 8cm is equal to the length of an arc of a semicircle with diameter of 16cm. I know this to be true but it just surprises me every time I see it.

I’ve added in the slide with AREA of semicircles too but just so students can see that area is affected differently to perimeter when scaling the diameter.

Curves

### Like this:

Like Loading...

With the cuboid exercise at the top, is there a quick way? I’ve compared sides and can see that the ratios add to 1 (if your compare the sides of each one to the first one; except the last) but I wouldn’t say it was quicker. What am I missing?

BTW, I love your stuff! You obviously give it some deep thought…..and gives me much deeper thinking as well. Keep up the brilliant work. This is by far my favorite math site.

LikeLike

Kind words. I’m not sure about quick ways. I love different methods though. Especially ones I haven’t consisted.

LikeLike