Sample team assignment

1. Give an example of a polynomial in one variable that has at least two integer roots.
2. 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.
   1. rabbit vs penguin
   2. rabbit vs hedgehog
   3. otter vs raccoon
   4. chipmunk vs rabbit
   5. chipmunk vs penguin
   6. rabbit vs raccoon
3. Give an example of some scary-looking math.

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Team A1

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

(1)

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

Comments:

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Team A2

1. 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.
2. 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.
3. Tensor algebra always makes for some terrifying-looking equations. Take this:

(2)

\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:

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Team A3

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

Comments:

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Team A4

Insert work for Team A4 here.

Comments:

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Team A5

Insert work for Team A5 here.

Comments:

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Team A6

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

(3)

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

Comments: