# IntMath Newsletter: Arc length of paraboloid spiral, brain injury to math genius

By Murray Bourne, 18 Jun 2014

18 Jun 2014

In this Newsletter:

1. Arc length of a spiral around a paraboloid

2. Padgett - from brain injury to math genius

3. Thank you, volunteers!

4. Math puzzles

5. Final thought - Asking good questions

## 1. Arc length of a spiral around a paraboloid

What is the length of a spiral around a paraboloid? This is an interesting application of integral calculus, involving an environmentally friendly cooker design. |

## 2. Padgett - from brain injury to math genius

This is a fascinating story. Jason Padgett was attacked by 2 men one night and savagely beaten. He ended up with severe concussion and an amazing new ability to "see the world through the lens of geometry". See the full story at: Brain Injury Turns Man Into Math Genius |

Don't miss the gallery of his art while you're there.

## 3. Thank you, volunteers!

Last mail I asked for volunteers to help transcribing some calculus videos on IntMath.

Thank you very much to Abby, Rusty, Li-sa, Kok Soon, and Suzanne for helping out. Good job and much appreciated.

## 4. Math puzzles

The puzzle in the last IntMath Newsletter involved a bet between Brigette and Ric, concerning cars.

Correct answers with explanation were given by Tomas, Saikrishna and Michael, giving a good insight into the thought processes they used.

**New math puzzle**: A box contains 20 balls numbered 1 to 20. What is the probability that any two of these balls chosen from the box will have numbers that are relatively prime?

Leave your responses here.

## 5. Final thought: Asking good questions is a vital skill

A lot of people who write to me have trouble articulating where their confusion lies. In class, a lot of students shy away from asking questions because they don't want to look stupid.

A common theme here is that students often don't have the skills to ask questions.

Dan Rothstein and Luz Santana in the book *Make Just One Change: Teach Students to Ask Their Own Questions* make the following crucial point:

The skill of being able to generate a wide range of questions and strategize about how to use them effectively is rarely, if ever, deliberately taught.

Asking good questions is essential for effective learning. When was the last time you were in a math class that taught how to ask good questions?

Until next time, enjoy whatever you learn.

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