
If you look around you, you can find many examples of mathematics
in nature’s designs. The shell of a chambered nautilus is
one of many examples that can be found. This shell takes on its
spiral shape because of the nautilus’s growth pattern and
the formation of small chambers of increasing size.
One method for studying the spiral is to use a set of right
angles winding around a point to represent the shape of the
spiral. These right triangles are drawn so that the sides used
to represent the spiral all have the same length. The longest
side of each right triangle is called the hypotenuse. The relationship
between the measures of the sides of the right triangles is
the basis for the Pythagorean Theorem.
The next time you see a daisy, sunflower, pineapple, pinecone,
or even the horns of a ram, see if you can find the spirals
that are part of their design.
Upon completion of the activities
in this unit, you should be able to:
 Use the following terms in a written paragraph to describe the
key concepts of this unit.
 hypotenuse
 Pythagorean Theorem
 radical sign
 radicand
 square root
 Simplify rational square roots.
 Find approximate values for square roots.
 Use the Pythagorean Theorem.
 Simplify square roots and radical expressions containing variables.
