## SIAM Undergraduate Research Online (SIURO)

## Volume 1, Issue 1

http://dx.doi.org/10.1137/siuro.2008v1i1

*Click on title to view PDF of paper or right click to download
paper. *

#### Undergraduate Student Research

## A Simple Expression for Multivariate Lagrange Interpolation [PDF, 414KB]

Published electronically July 2, 2008.

http://dx.doi.org/10.1137/08S010025

**Author: **Kamron Saniee (New Providence High School, New
Providence, NJ)

**Sponsor:** Richard Glahn (New Providence High School,
New Providence, NJ)

**Abstract:** We derive a simple formula for constructing
the degree *n* multinomial function which interpolates
a set of {n+m \choose n} points in R^{m+1},
when the function is unique. The formula coincides with the standard Lagrange
interpolation formula if the points are given in R^{2}.
We also provide examples to show how the formula is used in practice.

## Testing for the Benford Property [PDF, 341KB]

Published electronically July 2, 2008.

http://dx.doi.org/10.1137/08S010098

**Author: **Daniel P. Pike (School of Mathematical Sciences,
Rochester Institute of Technology, Rochester, New York)

**Sponsor:**
David L. Farnsworth (School of Mathematical
Sciences, Rochester Institute of Technology, Rochester, New York)

**Abstract: **Benford's Law says that many naturally occurring
sets of observations follow a certain
logarithmic law. Relative frequencies of the first significant digits k are
log(1 + 1/k) for k = 1, 2,
..., 9, where the base of the logarithm is ten. Financial and other auditors
routinely check data
sets against this law in order to investigate for fraud. We present the principal
underlying
mechanism that produces sets of numbers with the Benford property. Examples
in which each
observation consists of a product of variables are given. Two standard statistical
tests that are
useful for testing compliance with Benford's Law are outlined. A new
Minitab macro, which
implements both statistical tests and produces a graphical output, is presented.

## The Potential of Tidal Power from the Bay of Fundy [PDF, 18MB]

Published electronically July 11, 2008.

http://dx.doi.org/10.1137/08S010062

**Author: **Justine M. McMillan and Megan J. Lickley (Department
of Mathematics & Statistics, Acadia University, Wolfville, NS, Canada)

**Sponsor:** Richard Karsten and Ronald Haynes

**Abstract: **Large tidal currents exist in the Minas Passage, which
connects the Minas Basin
to the Bay of Fundy off the north-western coast of Nova Scotia. The strong currents
through this deep, narrow channel make it a promising location for the generation
of electrical power using in-stream turbines. Using a finite-volume numerical
model,
the high tidal amplitudes throughout the Bay of Fundy are simulated within a
root mean square difference of 8 cm in amplitude and 3.1^{o} in phase.
The bottom friction in the Minas Passage is then increased to simulate the presence
of turbines and an estimate of the extractable power is made. The simulations
suggest that up to
6.9 GW of power can be extracted; however, as a result, the system is pushed
closer
to resonance which causes an increase in tidal amplitude of over 15% along the
coast
of Maine and Massachusetts. The tides in the Minas Basin will also experience
a
decrease of 30% in amplitude if the maximum power is extracted. Such large changes
can have harmful environmental impacts; however, the simulations also indicate
that
up to 2.5 GW of power can be extracted with less than a 6% change in the tides
throughout the region. According to Nova Scotia Energy, 2.5 GW can power over
800,000 homes.

#### Expository

## Moving Forward by Traveling in Circles [PDF, 735KB]

Published electronically August 22, 2008.

http://dx.doi.org/10.1137/08S010050

**Author:** Stuart Boersma (Central Washington University)

**Abstract: **The purpose of this paper is to introduce the reader
to the mathematical construct
known as *holonomy*. Holonomy is a measurement of the change in a certain
angle as one travels along a curve. For this paper, we will consider two physical
situations
which involve "traveling in a circle" and comparing an
initial and final measurement
of an angle. In the first case we will see how this angular displacement can
be used
to prove that the Earth rotates! In the second example we explore the workings
of a
nineteenth century cartographic instrument. In both cases, traveling in circles
yields
interesting mathematical information.