Sample team assignment

- Give an example of a polynomial in one variable that has at least two integer roots.
- Pick
**one**of the following pairs of animals and identify which is cuter.*Each team must choose a part that no other team has yet answered.*- rabbit vs penguin
- rabbit vs hedgehog
- otter vs raccoon
- chipmunk vs rabbit
- chipmunk vs penguin
- rabbit vs raccoon

- Give an example of some scary-looking math.

# Team A1

- $x^2 + x$ is a polynomial that is zero when $x=0$ and when $x=-1$.
- Our team chose to compare rabbits with raccoons. Raccoons are cuter because it looks like they're wearing little masks.
- Here is some scary-looking math:

\begin{align} \int_{\partial \Omega}\omega=\int_{\Omega}\mathrm {d}\omega \end{align}

*Comments:*

# Team A2

- Consider the polynomial $x^2-2x-3 = (x-3)(x+1)$. It's clear, once the polynomial is placed in factored form, that $x=3$ and $x=-1$ are both roots of the polynomial.
- We looked at rabbits vs penguins. Penguins are cuter when they are babies but the adults are probably not as cute as an average rabbit.
- Tensor algebra always makes for some terrifying-looking equations. Take this:

\begin{align} \Delta(x_1\otimes\dots\otimes x_m) = \sum_{p=0}^m \sum_{\sigma\in\mathrm{Sh}_{p,m-p}} \left(x_{\sigma(1)}\otimes\dots\otimes x_{\sigma(p)}\right)\otimes\left(x_{\sigma(p+1)}\otimes\dots\otimes x_{\sigma(m)}\right) \end{align}

*Comments:*

# Team A3

- $x^2=x$ is true for $x=0$ and $x=1$.
- We chose rabbits vs hedgehogs. Rabbits are more cute because they have long ears.
- As far as math that looks scary, how about something that is obviously wrong? An example would be $0=1$. That is scary.

*Comments:*

# Team A4

Insert work for Team A4 here.

*Comments:*

# Team A5

Insert work for Team A5 here.

*Comments:*

# Team A6

- The zero polynomial has every real number as a root, and hence definitely has at least two integer solutions.
- For chipmunks or rabbits, they are at the same level of cuteness because they are both rodents.
- It's kind of scary that $\pi^2$ is equal to the sum of a relatively straightforward infinite series:

\begin{align} \frac{\pi^2}{6} = \sum_{i=1}^\infty 6/i^2 \end{align}