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

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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.

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

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