Birthdays are special days to celebrate. Every year we grow older, we place an additional candle on our birthday cakes to symbolize the fact that the Earth has traveled one more orbit around our daystar, the Sun.
How many candles will be on your birthday cake for your next birthday? What about the number of candles for the birthday cakes of your brothers and sisters, your parents, and grandparents? Do you have enough candles for all your relatives and friends?
Rather than running to the store for more candles for every birthday party, here is a fun way to make a single birthday candle become enough candles for even your great-grandparents' birthday cakes without having to call the fire department or having the first candles melt away before the last candles are lit.
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Remember before you start this activity, you will be using matches or lighters to light candles. Matches and lighters should only be used with close adult supervision. Your adult supervisor will learn something from this activity, too, and it is always more fun to share in the learning of new things.
This activity also uses mirrors. Mirrors are usually made of glass. If you should accidentally break a mirror, the only "bad luck" you will have is if you try and pick up the sharp pieces by yourself.
For the Birthday Mirror Math activity you will need the following items:
1. two flat mirrors (not the curved magnifying kind); square or rectangular mirrors work best
2. one birthday candle
3. tape (masking, duct or clear tape will do)
4. matches or lighter
5. an adult assistant to light the birthday candle
If you want to make this activity more mathematical, you can get a calculator and a protractor.
To perform the Birthday Mirror Math activity you will make a simple device called the "mirror multiplier."
Step 1 - Place the front sides of the mirrors together.
Step 2 - Place tape all along a common edge of the two mirrors to act like a hinge to allow the mirrors to open like a book and move through an angle. Congratulations! You have made your Mirror Multiplier.
Step 3 - Place the Mirror Multiplier on a table with the tape hinge running vertically.
Step 4 - Open the Mirror Multiplier to make a 45-degree angle (half of a 90-degree or right angle). The Mirror Multiplier should be able to stay upright on its own; if not, use more tape on the hinge.
Step 5 - Place an unlit birthday candle between the two mirror sides of the Mirror Multiplier equally distant from the mirrors and about half way inside.
Step 6 - Look into the Mirror Multiplier. What do you see?
Experiment with the Mirror Multiplier. Can you make three candles? What do you have to do to make five candles? See if you can figure out a pattern between the size of the angle between the two mirrors in the Mirror Multiplier and the number of the candles. Stop reading and go experiment. Come back when you have a guess (your hypothesis) of what is going on.
Did you try the experiment? If you did not, go do the experiment - we will wait for you!
Welcome back. Did you find a pattern? Good!
OK, here is the pattern between the angle of the mirrors in the Mirror Multiplier and the number of candles you see.
A full circle has a measure of 360 degrees. A single mirror has an angle of 180 degrees and you see two candles
If you do the math of 360 divided by 180 you get 2, or two images. Do the math of 360 divided by 45 and you get 8, or eight images, like the first picture. Try 360 divided by 90 - go to your Mirror Multiplier and make the angle between the two mirrors a 90-degree angle, place in a candle. How many candles do you see? Right, 360 divided by 90 equals 4; you see four candles.
Your Mirror Multiplier with the help of a protractor also works in reverse. Move the mirrors in your Mirror Multiplier to make 12 candles. What angle is this? Well 360 divided by 12 equals 30. So the angle needed to make 12 candles is 30 degrees.
