Discussion Questions:
1) Identify the various component pieces of the installation. Be sure to look at the preliminary studies for this work (Notebook First Sketch, Maquette, Studies) in order to look at all the components.
2) Identify the title?s reference and why do you think the artist chose this title?
3) Review the statement ?all is number?. How has this been interpreted and what do you think this phrase means?
4) What is a Carpenter?s Square and what was it used for? Is it still used today? Hint: Look at a store bought math geometry set ? you will be surprised by what you see!

Image: Henry Saxe Notebook and First Sketch for "With Reference to Pythagoras", 1974
© Henry Saxe
no. 18483.5

In the sketch from the Notebook, the artist draws an initial Carpenter?s Square. The dimensions for the two legs are 57? and 98?. The hypotenuse is labeled 112?.
a) Check using Pythagorean Theorem how far those measurements are off, being as accurate as possible.
b) Express your answer as a percentage error of the true measure.

Image:
Maquette for "With Reference to Pythagoras", 1974
© Henry Saxe
no. 18483.6

Looking at the supportive studies for this work, you can see that the slats on the bottom of the piece begin with a Carpenter?s Square. Imagine that the largest of the Carpenter?s Squares is the one illustrated in the Notebook.
In mathematics, a Pythagorean Triple is a set of three positive integers a, b, and c, such that a right-angled triangle exists with legs a, b, and hypotenuse c. Another way of saying this is that there are three positive numbers a, b, c that satisfies Pythagorean Theorem. The hard part of these is making sure that they are integers (that is they work out ?cleanly? with no need for decimals or rounding).
How many Pythagorean Triples are there with legs less than 57 and 98? Imagine these Pythagorean triangles working as Carpenter?s Squares in the pile of Notebook One.
Hint: One common triple is (3, 4, 5) and from this one you can get a whole bunch more including (6, 8, 10) and (30, 40, 50). Using a similar strategy can help you find the basic ones and then multiply them until you run out of space.

Image:
Study for "With Reference to Pythagoras", 1974
© Henry Saxe
no. 18483.3

One side of the installation has a grid pattern. Indicate using integer translations, how many ways there are to get from the bottom left corner to the top right using the grid pattern as indicated there. You may want to use the graph paper to illustrate that you have them all.

Image:
Study for Column Section "With Reference to Pythagoras", 1974
© Henry Saxe
no. 18483.2