Math Is Fun Forum

My tutor said I'd actually gone further with the investigation than he'd expected, so even though I didn't quite get the progressions part, it was still good enough to keep my grades in the higher section, so yay.

Thanks bobby.

Yep. If I want to find the length of the new square: a^2+b^2 = c^2

I love pythagoras

All my other sketchpad work is already at the top mark, and they take our work as a whole (it's partly creating resources as well as finding out for ourselves) so I am thinking that maybe I shouldn't be trying to work out all the complex maths if I don't really have tim (it's due tomorrow and I have an essay due Tuesday).

That maybe I should just comment that it is in successive geometric progression and just give one example

I love it.

Can I just say, Maths is Fun, that your website is amazing (only just found the accompanying forum) and I've been using it when I tutor to try and get my pupils to look on your website because it is so informative and easy to understand.

The exact wording isn't very clear. It says
Take a reqular ploygon
Dissect it in a way that leads to a smaller version of the same polygon
Repeat with the new polygon - the process can go on for ever.

The then gave some examples, the picture bobby kindly posted for me (without the red lines) demonstrates his example.

Then he writes:

What happens to the areas (ratios?)
What happens to the lengths of the sides?
Experiment with different starting polygons - do you always get the same ratios?

That's it. All he wrote. I'm doing it on geometer's sketchpad (which isn't the easiest program to use doing this)

Thanks guys for all your help.

Bobby, how did you work out those figures? We've not actually been taught any of this.

It's sort of like that bob, except I have 4 versions of each shape, each one where the dividing spiralling is at the same distance - so one is always at the half way mark, the next is always a third of the way in etc. And it's Square, Triangle and Hexagon

The actual question stares What happens to the areas? (ratios)
What happens to the lengths of the sides?
Experiement with different starting polygons - do you always get the same ratios?

Maybe I'm making it more complicated than it has to be, and I don't need to find a link with each separate shape, only that within each shape the areas have the same ratios. But I am aiming for the top marks

I have the link. It most let me post it
Still keeps telling me I have to be a member to post links.

I found the ratios by dividing the bigger area by the smaller area.

The picture below is an example of what I am doing. This is the triangle directed at half way along the edge The problem with what you are saying, bob, is that as you can see by the red line, the length of P-Q is more than 1 third and less than 2 thirds of the length. So it isn't as easy a ratio as you said.

THIS IS REALLY INFURIATING. I still can't post pictures, but I've done 10 posts.

I really need you to see it or it won't name any sense

Genius. Smart people