Geometry In Design - McGraw-Hill Ryerson

Achievement Check
14. Anwar claims that a hexagon does not need to be regular to tile
the plane. He says that any hexagon that has opposite sides equal
will work.
a) Draw a hexagon with opposite sides equal. Be sure to use three
different lengths in your drawing.
b) Determine whether your hexagon can be used to tile the plane. If
it can, show how it can be done. If it cannot, explain why not.
Extend
C
15. An architect is designing a window using the golden ratio.
a) The longer side measures 2.5 m. To the nearest tenth of a metre,
what should be the length of the shorter side
b) Draw a sketch of the window. Cut the window in half using the
midpoints of the lengths. Compare the ratios of sides of one of the
smaller rectangles. What do you notice
16. Many countries use international paper sizes, such as ISO A4. A sheet
of A4 paper measures 29.7 cm by 21.0 cm. This size is sold in Canada
at office supply stores. Obtain a piece of A4 paper, or make one from
a larger piece of paper.
a) Find the ratio of the length to the width, and record it.
b) Fold the paper in half across a line joining the midpoints of the
lengths. Measure the length and width of the folded paper. Find
the ratio of the length to the width.
c) Fold the paper again. Find the ratio of the length to the width of
the folded piece. What do you notice
d) The ratio of length to width for the ISO standard is always √ __
2 : 1.
Use a calculator to compare this ratio to the ratios that you found.
17. Use pencil and paper or software, such as The Geometer’s Sketchpad®,
to design fabric with a tessellation print. The fabric should appeal to a
person with a particular career or hobby, such as a musician, a golfer,
a pilot, a nurse, etc. Be sure to use basic geometric shapes to form a
more complex shape. Be creative in your selection of colours.
6.1 Investigate Geometric Shapes and Figures • MHR 15