The Pythagorean Snail Project
You will use a protractor and ruler to create a poster of the
Pythagorean Snail. All sides of all 17 (if they measure correctly, they
can get 18 triangles, but I require 17) triangles will be labeled. It
needs to be creatively decorated and colored. You may do the
calculations on the back in pencil, or on another sheet of paper. All
work must be shown and turned in on time to receive full credit.
Step 1: Place the paper in landscape orientation. Measure from the
top left hand corner 27.5 cm to the right and 20.5 cm down from the
top. This will be your starting point.
Step 2: Using your ruler draw a segment that is 7 cm long that
begins at your starting point and goes towards the left side of your
paper. Then measure 90° so that the vertex of your 90° angle is the
starting point. Draw a segment from the starting point that is 7cm
long, goes toward the top of the paper, and is perpendicular to the
original segment. Connect the endpoints of the two segments to
create a right isosceles triangle.
20.5 cm
↓
7 cm
27.5 cm
→
7 cm
Step 3: On a separate sheet of paper, use the Pythagorean Theorem
to calculate the length of the hypotenuse. Show all work and write
your answer in simplest radical form.
Step 4: Using the hypotenuse of the 1st triangle, create another right
triangle on top of the previous hypotenuse. The old hypotenuse will
be the new base and construct a perpendicular segment to this, with
the length of 7 cm. Then connect the two segments to form a new
hypotenuse.
Step 5: On your separate piece of paper, show the calculations to
find the length of the new hypotenuse.
Step 6: Continue to repeat this process of connecting and
constructing new triangles with a side of 7 cm, using the previous
hypotenuse as the other side. Continue to show your calculations on
your separate piece of paper. Construct triangles until you have 17.
This should form a full spiral snail.
Step 7: Detail your Pythagorean Snail with one or more designs.
Use color and creativity to create you picture.