Unit 1: Patterns and Numbers in
Figures
1.1.6 Wheel of Theodorus Task
• Step 1: Hold the index card with a corner on the vertex of the
isosceles right triangle on your worksheet, and mark the length of
each of the legs on the index card. This measurement represents one
unit, the length of the legs of the starting triangle.
• Calculation: Use the Pythagorean Theorem ( a2 + b2 = c2 ) to find the
length of the hypotenuse. Leave the length of the hypotenuse in
radical form. Fill in its measurement in the table and write the
measurement on the hypotenuse on the worksheet.
• Step 2: Place one side of the index card along the hypotenuse, with
the corner at point A. Use the 1 unit measurement marked on the
card to draw a leg for a new triangle, then connect that leg to point B,
making a new right triangle.
• Calculation: Fill in the measurements of the legs of the new triangle
in the table, then use the Pythagorean Theorem to calculate the
length of the hypotenuse. Leave the length of the hypotenuse in
radical form. Fill in the measurement of the hypotenuse in the table
and write it on the triangle in your drawing.
Continue adding triangles until you have a total of 9 in your
spiral. Fill in the measurements in the table for each one, and
write the length of the hypotenuse on each triangle in your
drawing.
Triangle
1 2 3 4 5 6 7 8 9
Number
Leg 1
1 1 1 1 1 1 1 1 1
Length
Leg 2
Length
1 2 3 2 5 6 7 8 3
Hypotenuse
Length 2 3 2 5 6 7 8 3 10
• Use your observations to predict the length of the hypotenuse of the
28th triangle.
• Use this prediction to write a formula for the nth triangle.
• Calculate the areas of the first five triangles and complete the table
below. Leave the areas in radical form.
Triangle
1 2 3 4 5
Number
Triangle
Area
• What would the area of the 28th triangle be?
• Write a formula for the area of the nth triangle.
• Calculate the perimeters of the first five triangles and
complete the table below. Leave the perimeters in radical
form.
Triangle
1 2 3 4 5
Number
Triangle
Perimeter
• What would the perimeter of the 28th triangle be?
• Write a formula for the perimeter of the nth triangle.
• Extension Project (SEE TITLE SLIDE)
• The Wheel of Theodorus makes a nice beginning for an art project.
Starting with any size isosceles right triangle, create a picture with the
Wheel of Theodorus as its foundation. If you would like to see some
example pictures, go to the following website:
•
• http://www.ldlewis.com/Teaching-Mathematics-with-
Art/Wheels.html
Homework
• pp. 38 – 40
•
• 1, 2, 4, 5, 7 – 25 odd, 30, 32