# Pullback - a mathematical puzzler

• carltrembath
In summary, the pullback of xdy can be expressed as r*cos(alpha)*cos(beta)*dy + r*sin(alpha)*cos(beta)*dx.
carltrembath
Hi y'all. Carlo T here with a little mathematical puzzler.

Here's the big ol' question, are you folks ready?

let phi:(0, infty)x(0, 2*pi)x(-pi/2, pi/2)->R^3 be defined by
phi(r,alpha,beta)=(r*cos(alpha)*cos(beta), r*sin(alpha)*cos(beta), r*sin(beta)).

Calculate the pullback phi*(xdy)

I've calculated phi*(dx), phi*(dy) and phi*(dz) but am not sure where to go from here.

For example, is there a way of rewriting phi*(xdy) using one of the pullback properties?

Get your noggins round that one brothers.

Peace out, from the C to the T to the remBath!

The pullback of xdy is given by phi*(xdy)=phi*(dx)*dy + phi*(dy)*dx. We can expand this as phi*(xdy) = r*cos(alpha)*cos(beta)*dy + r*sin(alpha)*cos(beta)*dx.

## 1. What is Pullback - a mathematical puzzler?

Pullback is a mathematical puzzle game that involves plotting points on a grid to create a path from a starting point to an end point.

## 2. How do you play Pullback?

To play Pullback, you need to place numbered tokens on a grid to create a path from the start point to the end point. The numbers on the tokens represent the number of spaces the token can move horizontally or vertically. The goal is to use all the tokens and reach the end point in the fewest number of moves.

## 3. What skills does Pullback help develop?

Pullback helps develop spatial reasoning, critical thinking, and problem-solving skills. It also improves hand-eye coordination and fine motor skills.

## 4. Is Pullback suitable for all ages?

Yes, Pullback is suitable for all ages. It can be played by children as young as 6 years old and can also be challenging for adults.

## 5. Are there different levels of difficulty in Pullback?

Yes, Pullback offers different levels of difficulty, ranging from easy to expert. The higher the level, the more challenging the puzzles become.

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