BrainDen.com - Brain Teasers
• 0

# How much white?

## Question

The area of the triangle is 1. What is the area of the white portion?

## Recommended Posts

• 1
Spoiler

This looks like a Sierpinski triangle. It can be defined iteratively by removing the "middle triangle" from the figure, then the "middle triangles" of the remaining 3 triangles, then the middles of those...

At each step, the shaded portion is 3/4 of what it was before. So the area of the remaining shaded portion after N steps is (3/4)N. If continued ad infinitum, the limit is zero. Therefore the area of the shaded portion is zero, and the white portion must then be 1.

##### Share on other sites
• 0

Area of white  to 3 places is  = 0.763

##### Share on other sites
• 0

Area of the white is = 1 (1/4) + 9(1/4 x 1/4 ) + 27 ( 1/4 x 1/4 x 1/4) + 81 ( 1/4 x 1/4 x 1/4 x 1/4 )  The lowest common multiple of all of the divisors  is 1024 or 4 x 4 x 4 x 4

Area of the white is =  256/1024 +  192 / 1024 +144/1024 +108/1024 + 81/1024;  Totaling these =781 / 1024  then dividing 1024 into 781 you get 0,762695313 rounding off to 3 places = 0.763

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×