*A,*on a sheet of paper. Cut out the circle. Mark a random point

*B*anywhere on the circle. Then, fold … Continue Reading ››

Of all the conic section construction techniques, my favorite is undoubtedly the approach that requires nothing more than a paper circle.
Here's what to do: Draw or print a circle and its center, point *A,* on a sheet of paper. Cut out the circle. Mark a random point *B* anywhere on the circle. Then, fold … Continue Reading ››

In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip's path as you pull the pencil around the taut string. Guaranteeing that the traced … Continue Reading ››

In my prior blog posts, I've described how to construct ellipses using linkages, concentric circles, congruent triangles, and tangent circles. These are all great methods, but I think I got ahead of myself: There's a simple ellipse … Continue Reading ››

The 17th-century Dutch mathematician Frans van Schooten developed "hands-on manipulatives" centuries before the term became popular in math education circles. Below are two images of ellipse-drawing linkages from van Schooten's manuscript, *Sive de Organica Conicarum Sectionum in Plano Descriptione, Tractatus* (*A Treatise on De**vic**es for Drawing Conic Sections*).
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In the early 1990s, Danny Vizcaino, a high school student at Monte Vista High School in California, wrote to Key Curriculum Press noting that Sketchpad did not come with a tool to draw an oval. Undaunted by this omission, Danny had built his own oval with the software and shared it with Key's editors.
As shown in the interactive … Continue Reading ››

Welcome back to my ongoing series in which I feature interactive Web Sketchpad models that draw conic sections. Today’s installment, like the previous one, focuses on ellipses, and dates back to the 17th-century Dutch mathematician, Frans van Schooten.
Below is an image from van … Continue Reading ››

This will be the first in an occasional series of posts that offer interactive Web Sketchpad models for drawing conic sections. My interest in conic sections dates back to the mid 1990s, when I authored a conic sections book for Key Curriculum Press . That book is Continue Reading ››

As a student, I didn’t place conic sections on my list of favorite high school topics. The standard textbook treatment of the ellipse, parabola, and hyperbola seemed uninspired. There were messy algebraic equations with multiple square roots. There was lots of terminology. Drawing a conic meant plotting several points on graph paper and connecting them with … Continue Reading ››