#14 Extend and Connect

Extend and Connect

Put two mirror books next to each other to form a square “room” with mirror walls. Look inside from the top, to find infinity. Next, try a triangular mirror room – does it work the same?

Find all multiplication tables hidden in the mirror book. Open it ninety degrees for times four, seventy-two degrees for times five, sixty degrees for times six, or just count reflections. Even three-year-olds can intuitively find (if not necessarily measure) the angles that turn one toy into three toys, or four toys, in the mirror book.

Draw a line across the opening of the mirror book and start closing the book. Your line will form polygons with more and more sides. If you manage to make the opening in the mirror book infinitely small, your polygon will turn into a circle! As with all other ideas that relate to infinity, kids and grown-ups find this deeply meaningful. The idea that polygons approximate circles as the number of sides grows inspired authors of several math adventure books, such as the classic “Flatland” and “The Greedy Triangle.”

Where in science and technology are angles of mirrors important? Help the child change angles of car mirrors. Look inside physical or virtual telescopes and microscopes. Ask a dentist to explain how mirrors help to see inside the mouth. Watch a video about solar sails.