UPDATE: The article is now published. Read it in *Mathematics Magazine.*

Yesterday I posted an article to the arXiv, “A Trisectrix from a Carpenter’s Square.”

Abstract: *In 1928 Henry Scudder described how to use a carpenter’s square to trisect an angle. We use the ideas behind Scudder’s technique to define a trisectrix—a curve that can be used to trisect an angle. We also describe a compass that could be used to draw the curve.*

I also made a GeoGebra applet to accompany the article. Give it a try.

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I played around a bit with your Carpenter’s Trisectrix. The curve has the following paremetrizations:

for and

for .

The "drop" part of the curve is given by or .

The drop has area . The perimeter can be written using Elliptic functions (approximately 4.12).

If the drop of the curve is considered to be the cross-section of a solid of revolution, its volume is and its surface are is .

Cool! Thanks. My first approach was to parametrize the curve. I parametrized it in terms of the slope of one of the legs of the T (actually I parametrized it both ways) and used that to find the non-parametrized version. Then I came up with this other approach that didn’t require going through the parametrization. I didn’t go the trig route. Thanks!