This post is by Jason Moses, who has been an enthusiastic explorer in the Mathematical Curiosities Program. Read on to understand what perfect rulers are, and look at his creations. What follows are all Jason’s words.
In a regular ruler, markings are placed at regular intervals from each other. But are all these marks needed? No, not at all. A ruler, where all unnecessary marks are removed, yet all numbers can still be measured is called perfect ruler.
An example of such a ruler is an 8 cm ruler with only 3 marks- only points 2, 4 and 7 are marked on it. But all numbers until 8 can be measured using it. The starting point is taken as 0 and the end is 8, since this is a 8 cm ruler. Here’s how you can measure all numbers unto 8 using this: 1 (8-7), 2 (4-2), 3 (7-4), 4 (4-0), 5 (7-2), 6 (8-2), 7 (7-0), 8 (8-0).
There are multiple 8 cm perfect rulers you can make, I found 4 other such possibilities. These are models of the rulers that I made.
You may ask- “Why would I need such a ruler?”. Well, if you want to mark each unit on the ruler that’s fine, but a normal ruler is so booorring for a math lover!
Perfect rulers can be fun! “Fun?”, I hear you ask doubtfully. Yes, you can create many fun games using the principle of the perfect ruler. Here is one such game called the ‘Adder’, which I designed.
The adder is a 15cm long scale, shaped like a snake. The adder has 5 stripes on its body. These stripes are 1,3,5,8 and 14 units away from the base of the adder’s head. Your goal is to measure all distances up to 15cm by folding along these 5 stripes. Challenge accepted? You guys are an adventurous lot!
WARNING:-Do not use a real “adder” for this activity, instead use a strip of paper.Here is an adder template for you, so you don’t have to go adder hunting! 😉
Do try making your own games based on the “perfect ruler” and share your ideas in the comments section. I promise you it will be FUN!
This activity has been adapted from the amazing work done by the people at Math Teacher Circles.