Categories

# The holy number

An equilateral triangle and several line segments. What fraction is purple?

Scroll down for a solution to this problem.

## Solution

The purple fraction is 1/7.

## Poem

The holy number
It could be 777
Straight across and right from heaven
Or maybe another one
But it could be a number
The golden ratio
That’s not even a 0
Known from Pythagoras and Euclide
The golden number in geometry
A number that’s holy
For thinkers, poets in each century

Bella

# Donβt miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.

## One reply on “The holy number”

Sanjay Godsesays:

ABC equilateral triangle with AB top horizontal side. D midpoint of AB. E midpoint of DC. F is point on AE and DF perpendicular to AE.
Triangle DFB = triangle ADF.

AD=1, DE=β3/2. Hence AE=β7/2

Triangle ADE = (1/2)*AD*DE = (1/2)*DF*AE giving DF=β3/β7

Hence AF=2/β7 from triangle ADF

Area of triangle ADF=(1/2)*AF*DF=β3/7

Area of triangle ABC=(1/2)*AD*DC=β3

Hence the proportion is (β3/7)/(β3)=1/7 or 0.142857