Author Archives: jtolpin

Pondering Polygons

There are a number of geometric constructions that allow us to create regular (i.e equal-angle and equal-facet length) polygons. Most of those for squares, rectangles and triangles are quite straightforward, requiring  but a few steps. However, those dealing with five … Continue reading

Posted in Uncategorized | 4 Comments

The Graphic Rule

This excerpt from our latest book, “From Truths to Tools,” speaks to a rather esoteric, but highly useful, rule for use with scaled drawings: Here’s a typical, traditionally drawn small boat plan: To find the dimension of any particular part … Continue reading

Posted in From Truths to Tools, Uncategorized | 9 Comments

From Point to Person

Among Renaissance-era artists, man was often framed within geometric shapes, most commonly (and most famously) squares and circles. However, humans are five vertex creatures (as are the majority of living organisms), a fact that perhaps lead other artists to depict … Continue reading

Posted in Uncategorized | 19 Comments

The Hidden Hexagon

You may remember this page from the introduction to “From Truths to Tools“: We’ve had a few folks ask about the “hidden hexagon” mentioned in the text, and we think it’s time to share the answer with everyone. This also … Continue reading

Posted in From Truths to Tools, Uncategorized | 38 Comments

Geometry in Time for the Holidays

In the spirit of the holidays, let’s perform some simple, ancient geometry to create the iconic symbols of the two religions celebrating major holidays this month. You’ll need only a compass, a straightedge, a piece of paper and a couple … Continue reading

Posted in From Truths to Tools, Uncategorized | 8 Comments

Divide This!

…says the Italian renaissance astronomer Galileo Galilei to a young student as he demonstrates a pair of proportional dividers. So how do these ingenious scaling devices work? The answer is embedded in the geometry of the sectioning of a circle. … Continue reading

Posted in Uncategorized | 5 Comments

Solving Spans with Sticks, Strings, Sightlines & Stones

In this excerpt from our book, “From Truths to Tools,” we show how the carpenter/geometers of antiquity used the simplest of tools – those mentioned with almost annoying alliteration in the title – to solve for an unknown distance.    … Continue reading

Posted in From Truths to Tools, Uncategorized | 4 Comments