## Archive for October, 2011

### Kemper Art Museum

October 25, 2011

The club will take a trip to the Mildred Lane Kemper Art Museum on the campus of Washington University to view and discuss the current installation Tomás Saraceno: Cloud-Specific.

Tomás Saraceno (Argentina, b. 1973) is internationally recognized for his fantastic architectural proposals, pneumatic sculptures, and environmental installations. Cloud-Specific showcases a selection of the artist’s latest inflatable sculptures, prototypes, and video work, all linked to his investigations into new modules for living that respond to the challenges of climate change and other social and environmental concerns.

We will gather in the Ritter Hall lobby and then organize into cars for the short trip to the museum. We expect to return to the SLU campus by 5:00pm.

### 4-dimensional Hypercubes

October 24, 2011

The picture above is a drawing of a 4-dimensional hypercube. In general, we can define an n-dimensional hypercube for n a non-negative integer. The first 4 of these are

0: A point
1: A line segment
2: A square
3: A cube

We construct higher dimensional hypercubes from lower dimensional ones. We start with a 0-dimensional hypercube: a point.

Start with a point A and draw a line to a different point B. Let’s say the distance between A and B is d. This is a 1-dimensional hypercube: a line.

Now draw a line of length d, orthogonal to AB, from B to a point C, and a line of length d, orthogonal to AB, from A to a point D. This is a 2-dimensional hypercube: a square ABCD.

Now draw lines of length d respectively from each corner of the square ABCD, orthogonal to both AB and BC. Call the terminal points E,F,G,H. This is a 3-dimensional hypercube: a cube ABCDEFGH.

And so on for higher dimensions.

Drawing these on a piece of paper, a 2-dimensional plane, becomes more difficult as n increases. For example, a picture of a 7-dimensional hypercube looks like

How do we draw these pictures? In the 4-dimensional case, we can draw a hypercube from these steps. To get a better idea of the hypercube, we can watch the hypercube rotate

or rotate it ourselves.

### Function Bingo!

October 18, 2011

The Math/CS club invites you to play Function Bingo with them on Wednesday, October 19 from 4:00pm to 5:00pm in the lobby of Ritter Hall. There will be prizes of the fabulous variety awarded to the winners!

How do you play function bingo? It’s just like boring old regular bingo, but with an exciting twist: Calculus!

Can you find where a function is increasing or decreasing? Concave up or concave down? If you can, join us as we serve you tea, coffee, and cookies as you play.

### Touch Mathematics

October 15, 2011

Touch Mathematics is a website that has interactive tools for the trigonometric functions and derivatives of certain functions.

Touch Mathematics – Trigonometry

The trigonometry tool shows the graphs of the six trigonometric functions $\sin\theta, \cos\theta, \tan\theta, \csc\theta, \sec\theta,$ and $\cot\theta$. You can go around the unit circle and compute the values of the these functions at different angles as well as move along the graphs of the functions in the xy-plane.

Touch Mathematics – Derivatives

The derivatives tool shows the graphs of the first and second derivatives of the functions $x, x^2, x^3, \dfrac{1}{x}, \ln x^2, \sin x, \pi^x, e^x, \sin^{-1}x,$ and $\sqrt{x}$. You can trace along the graphs of the function, its derivative, and its second derivative. The tool computes the values of these functions as you trace along the graphs and displays the signs of the first and second derivatives.

### Second Annual Integration Bee Results

October 6, 2011

The eyes of the world were upon SLU’s Second Annual Integration Bee yesterday in the Ritter Hall lobby, where participants computed integrals for a chance to win fabulous prizes. It was a very exciting competition with nearly 20 participants.

The competition began with a set of 5 integration problems on a chalkboard. Participants had only 10 minutes to find solutions, but they were prepared. Their minds were sharp and their pencils swift (and vice-versa). Many advanced from this first round of the bee, making perfect scores.

It was clear that these were no ordinary integrators. No, these people were good. To thin out the set of competitors, the organizers gave them a tougher set of 5 problems.

This difficult set proved to be too much for most of our contestants. Only three people moved on: Wesley Gardner, Max Clifton, and Erica Zak.

Wesley had the top score, while Max and Erica were tied for second. We then had an exciting runoff between Max and Erica to compete against Wesley for the championship.

Max and Erica raced to solve the integral
$\int_0^\infty x^{10} e^x dx$
(Do you know what it is?)

Max was the first person to arrive at the correct answer and so moved on to face Wesley for the gold. (Ok, we didn’t really have actual gold for the winner. It was metaphorical gold.)

The stage was now set. Max. Wesley. Chalkboards. Chalk. The Championship Integral.
$\int \ln(\cos x)\tan x dx$

GO!

And the winner is…Wesley Gardner! Fabulous prizes were distributed and the world could rest easy for another year, knowing that the integration king of SLU has been crowned. (Again, we didn’t really have an actual crown.)

### The Second Annual Integration Bee

October 4, 2011

$\int f(x)dx = ?$

Think you’re the best integrator at SLU? Come and find out as the Math and CS club hosts the second annual integration bee in the Ritter Hall Lobby Wednesday at 4:00pm. You will be challenged to compute indefinite integrals under time constraints.

Fabulous prizes will be bestowed on the best integrators!