I-MATH

The Conics

(and other mathematical curves)

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Please do the GSP Lab Files, Chapter 10 Circles, in connection with this web page

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 not only allow students to see the relationships among mathematics, art, graphic design and architecture, but gives them opportunities to apply their imagination, creativity, and visual thinking skills. Please go to 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

http://www.fishrock.com/conics/

As you saw in the chapter on transformations, there are some beautiful geometric graphics that can be constructed based on mathematical curves, 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. The students should save their GSP files and then copy and paste the graphic into a painting program. It looks nicer if they first hide all points. (A quick way to select all the points to hide them is to click on the point tool in the tool box on the left side of the screen, then use the Edit menu to Select all Points. Then Hide Points in the Display menu.)

The instructions for constructing this Golden Spiral of quarter-circles can be found at the following link:

My E-School distance learning students have constructed some beautiful geometric graphics, many of which are based on mathematical curves, and you will find step-by-step instructions for constructing a graphic based on circles, at the following link: