Guest Post: GeoGebra Investigation of the Equiangular Spiral in the Flight of an Insect

If you are near an outside lamp after dark you will notice some insects spiraling around it. Are they simply attracted to the light?

If an insect positions its body in a certain direction and keeps a constant angle with the light rays coming from the Sun or the Moon (which are parallel), it will follow a straight line trajectory. However, people brought to the night sky electric lights emitting radial rays. The insects, continuing to follow the same way of orientation will keep a constant angle with the light rays, but this time they will not fly on a straight line. The trajectory will be an equiangular spiral.

Here are two GeoGebra applets modeling this phenomenon.

http://lima.osu.edu/people/iboyadzhiev/GeoGebra/FlightOfInsect.html

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Irina Boyadzhiev (author) is a lecturer in mathematics at the Ohio State University at Lima. Her GeoGebra applets are available at: 

http://lima.osu.edu/people/iboyadzhiev/MyGeogebra.htm

 

Link Post: Applying Mathematics to Web Design

“Mathematics is beautiful.” This may sound absurd to people who wince at numbers and equations. But some of the most beautiful things in nature and our universe exhibit mathematical properties, from the smallest seashell to the biggest whirlpool galaxies. In fact, one of the greatest ancient philosophers, Aristotle, said: “The mathematical sciences particularly exhibit order, symmetry and limitation; and these are the greatest forms of the beautiful.”

Because of its beautiful nature, mathematics has been a part of art and architectural design for ages. But it has not been exploited much for website design. This is probably because many of us regard mathematics as being antithetical to creativity. On the contrary, mathematics can be a tool to produce creative designs. That said, you don’t have to rely on math for every design. The point is that you should regard it as your friend, not a foe. For illustrative purposes, we created a couple of web designs that present mathematical principles discussed in this article. We are also giving away a couple of PSDs that you can use right away in your next design. Continue reading…

Steven Strogatz

Higher mathematics is always perceived as hieroglyphics by many — a language that can only be understood by experts.  There are many gifted mathematicians, who can solve extremely difficult mathematical problems, but there are only a few who have the gift to communicate mathematics to the masses.
One of the few mathematicians who has made excellent explanations about technical concepts is Steven Strogatz.   In New York Times’ Opinionator, he  wrote 15 articles about different topics in  mathematics, and his explanations were simply grand. » Read more
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