Vandal Science News-February 2015
Anything can inspire a good puzzle – even something as simple as a tile floor. You've probably seen a pattern of floor tiles like the one pictured here. It consists of squares and regular octagons (all eight sides are the same length and all eight angles measure 135 degrees). Suppose the area of each green octagon is 6 square inches. What then is the area of a pink square? Express your answer in the form a + squareroot(b) where a and b are integers.
The area of the pink square is sqrt(18) – 3, or 3(sqrt(2) – 1).
The first thing to do is calculate the area of the octagon in terms of its side length x. We can cut the octagon into a square, four triangles, and four rectangles as shown. The triangles are right triangles with hypotenuse of length x, so their legs must be length [sqrt(2)/2]x. So each of the triangles has area x2/4. Adding everything together, we see that the octagon has area
x2 + 4[x2/4] + 4x[sqrt(2)/2]x = 2x2[1 + sqrt(2)]
This gives us the equation
2x2[1 + sqrt(2)] = 6
(since we know the octagon has area 6). So
x2 = 3/[1 + sqrt(2)]
But x2 is exactly the area of the square tile, so all we need to do is simplify this number. A little work at that yields our final answer.
- Fred Burton (Mathematics, 1968)
- Greg Stenback (Geological Engineering, 1985; M.S. Statistics, 1987)
A Newsletter for Alumni and Friends February 2015
Dear Alumni and Friends of the University of Idaho College of Science,
There is so much going on right now that one hardly knows where to begin. This has been a period of tremendous faculty renewal in our ranks. Over a dozen new tenure-track, research, and clinical faculty have been added to the college over the past year and a half, and the changes have opened opportunities to refocus and build our strengths. Recent additions have buttressed strong profiles in synthetic and DNA chemistry and the broad area of systems biology, encompassing work from biophysics, biostatistics, and biomathematics.
There is a bumper crop of great research coming out of the College of Science right now, and you can read about some of that here in the Vandal Science News. For instance, you'll find a feature on Ebola-related research of an interdisciplinary faculty team. That project is part of a larger initiative – the Center for Modeling Complex Problems – which includes the “Collaboratorium”, a newly renovated campus site to facilitate interdisciplinary cooperation on important research questions.
But along with our successes in research, we will always preserve Idaho's student-centered focus and our commitment to educational quality. In fact, some of the innovation that goes on in our college is directed at how to best engage our students in the discovery of science. Professor Trish Hartzell from the Biological Sciences Department is currently leading a project (funded through the Howard Hughes Medical Institute) to integrate learning in our lab courses – with Biology and Chemistry lab students working together on projects that teach both disciplines.
And of course, we're as proud as ever of our work in promoting undergraduate research. In this issue of Vandal Science News you can read profiles of a couple of this year's winners of the Hill Undergraduate Research Fellowships.
Finally, I'll brag about how engaged our faculty and students are in the broader life of the university. From Faculty Senate leadership (the past two chairs have come from the College of Science!) to the great work done by our student ambassadors, you will find the College of Science working everywhere. We'll even have six of our faculty members delivering workshops in this month's Lionel Hampton Jazz Festival, promoting excitement for college attendance to the visiting high school students. In addition to the programs we've provided for several years in the mathematics and physics of music, we're adding one this year from biology – a workshop titled “What might be growing in my instrument?” Cool stuff indeed.
I hope you enjoy reading this brief survey of some of the exciting things going on. Look around our website (and the websites of our departments) for even more.
And as always, thank you for your continuing support of the College of Science.
- Dean Paul Joyce
In the Lab from Day 1
First-year student earns Hill Fellowship for work with microscopic nanosprings