# Questions for ‘Geometry can shape our world in unexpected but useful ways’

## SCIENCE

1. Come up with a one-sentence definition for the word geometry. Based on your definition, describe one type of problem that geometry could help someone solve.
2. Imagine you are tiling a bathroom with triangle-shaped tiles. Use a blank sheet of paper to sketch these triangle tiles in a pattern that could be used to tile a floor, completely. When you finish, there should be no gaps or partial tiles (except on the edges). Now, try the same thing with pentagon-shaped tiles. (A pentagon is a five-sided shape.) Were you equally successful with both tiles? Explain your answer by contrasting your success with both tile shapes.
3. Give an example of a three-dimensional (3-D) shape. For the shape you just provided, what would the 2-D equivalent of that shape look like?

1. What is the most stable arrangement for stacking oranges at the grocery store? How has this technique been used to improve radio communications?
2. How might a textbook’s two-dimensional (2-D) shadow be used to infer the details about the textbook’s three-dimensional (3-D) shape?
3. How is the problem studied by Casey Mann similar to the orange-stacking problem?
4. What is one way the problem studied by Mann differs from the orange-stacking problem?
5. By the early 20th century, how many types of pentagons had been discovered that could completely tile a surface?
6. What is a potential application of discovering tight-fitting pentagon shapes?
7. What is one example of geometric tiling strategies found in nature?
8. An icosahedron is a 3-D shape. How many faces does an icosahedron have? Each of these faces is shaped like an equilateral triangle. What is an equilateral triangle?
9. Give one example of a common or everyday item shaped like an icosahedron.
10.  What benefit does a capsid provide to a virus?