#MathProblemOfTheDay: Nike Running App

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Help me figure out how fast I ran!

I was gonna go for a walk and then decided to turn it into a yog. My routine was: walk a half mile, run a half mile. Repeat 4 times.

Nike Running┬átells me my average pace was a 14:17 minute mile. No magic there – they just took my total time (57:11) and divided it by my total distance (4 miles).

Anyway, here’s what happened. While I was walking I was relaxed. I was able to look at the screen and see my pace – about 19 minutes per mile. While I was running I had no energy or focus to spare – and I didn’t look at the screen. I want to find out roughly how fast I was running.

Given that my walking pace hovered around 19 minutes per mile, what was my average running pace?

#MathProblemOfTheDay: keeping warm in the snow

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Which position would keep you warmer?

The answer is probably intuitive to you. That’s why I love this image – it connects simplicity and intuition to a more complex topic: optimization.

Optimization is an example of applied calculus. It sounds all fancy but it can be expressed simply. You want to optimize one thing (in other words, maximize something you want, or minimize something you don’t want), while keeping another thing constant (this is called a constraint).

In this photo, I want to minimize surface area to keep warm. (Why will minimizing surface area keep me warm??) My constraint is my volume – I can’t change the size of my body. It stays constant no matter how I position myself.

Ok, now imagine we’re no longer dealing with the human body. Take a piece of clay. What would you mold it into, in order to minimize surface area? How do you know you’ve succeeded?