I-MATH
The Conics
I-MATH
The Conics
A number of the National Council of Teachers of
Mathematics Standards have to do with Connections and Applications of
mathematics. I have created a set of web pages for my own students,
to guide their study of mathematical applications. There are some
particularly interesting applications related to mathematical curves:
circles, ellipses, parabolas, hyperbolas, spirals and other curves.
These connections allow students to see the relationships among
mathematics, art, graphic design and architecture, They also gives
them opportunities to apply their imagination, creativity, and visual
thinking skills. You might be interested in the following web page,
and all the pages that are linked from this page:
The internet offers many opportunities for students to see real and current applications of the mathematics they are studying. The interesting graphic below is a representation of a mathematical curve, and came from a fascinating website called Conics: Human Shelter on Demand. This website offers unusual and mathematical designs for tents and shelters in the shapes of mathematical curves! The author says: "The following images are a quick peak at a new habitat design. By virtue of strength through flexibility, a conic is a true shell, able to withstand hurricane force winds and the most violent earthquakes. Coupled with energy and material saving designs, Conics are a habitat that can be built within the carrying capacity of our small planet. I invite you to explore the Conics web site and judge for yourself..." Chuck Henderson - Inventor
As you saw in the chapter on transformations, there are some beautiful geometric graphics that can be constructed based on circles, and using transformations. These graphics can be constructed using compass and straightedge, and then finished with colored pencils or pens. The Geometer's Sketchpad allows students to construct these graphics on the computer, and most painting programs can then be used to make stunning computer graphics, such as the one below:
The instructions for constructing this Golden Spiral of quarter-circles can be found at the following link:
My students created some beautiful "geometric graphics" using constructions. We were very excited when the National Council of Teachers of Mathematics were so impressed with our work that they published a poster book of the students' work!