- #1

mathmari

Gold Member

MHB

- 5,049

- 7

Hey!

A DIN A4 sheet is divided into thirds. A rectangle is the root of the tree, the other two rectangles are each divided into thirds again. Two rectangles form the branches - one to the left, one to the right - the others are again divided into thirds and so on.

View attachment 8105

I want to calculate the area of that tree. I understood teh mathod as follows:

First we have the whole sheet.

Then we divide it into three parts.

Then all except of $2^0=1$ part are again divided into three parts.

Then all except of $2^1=2$ parts again again divided into three parts.

Then all except of $2^2=4$ parts again again divided into three parts.

and so on I mean something like that:

View attachment 8106 So at level i of the tree we divide all parts except of $2^i$ into three parts. Have I undersood that correctly? (Wondering)

How can we calculate the area? Do we maybe have to write the above as a recursive function? (Wondering)

A DIN A4 sheet is divided into thirds. A rectangle is the root of the tree, the other two rectangles are each divided into thirds again. Two rectangles form the branches - one to the left, one to the right - the others are again divided into thirds and so on.

View attachment 8105

I want to calculate the area of that tree. I understood teh mathod as follows:

First we have the whole sheet.

Then we divide it into three parts.

Then all except of $2^0=1$ part are again divided into three parts.

Then all except of $2^1=2$ parts again again divided into three parts.

Then all except of $2^2=4$ parts again again divided into three parts.

and so on I mean something like that:

View attachment 8106 So at level i of the tree we divide all parts except of $2^i$ into three parts. Have I undersood that correctly? (Wondering)

How can we calculate the area? Do we maybe have to write the above as a recursive function? (Wondering)