SETH rectangles

All draw a rectangle

What size?

Any size

Now find it's Perimeter and it's area

Hey I get the same answers for this one !

What do you mean?

Can I draw it on the board? Look...

The Perimeter is 6 + 6 + 3 + 3 = 18 and the area is 3 x 6 = 18

What's your name ?

Seth Thompson

Then you're world famous now.... you've discovered the SETH RECTANGLE !

Right . Class .... hunt for more Seth Rectangles. Now!!

What do you mean?

Well that was a 3x6 Seth Rectangle. Can you get one of a different size? For instance does a 8x2 work?

No ... the Perimeter is 20 but the Area is 16

OK start the hunt for others....

I've found one .... look ...

That's rubbish!! It's the same as before. Just turned round. Isn't it?

If you say so. Found any others?

It's no good. We don't think there are any.

Let me look at what you've tried .... mmm ... all very random.

What do you mean?

OK All listen. Let.s start a SYSTEMATIC search. What could that mean?

In order somehow?

What order?

Well like trying all the 1 by somethings then the 2 by somethings and so on..

Well you said it so you try it. All check a 1x1 then a 1x2 then a 1x3 and so on. Now!

Hey I've spotted a pattern!

Let's see. What a confusing jumble. Put your results in a table so that I can see what you mean.

That's better. Let's put it up on the board:

Any comments?

The Area will never catch up with the Perimeter.

What does that mean for our search?

There will be none starting 1 by something. Can we try the 2 by something?

Don't let me hold you back!!