Interesting triangles


Pythagoras' Triangle

Mathematicians' favourite triangles are those with one
L-shaped corner.
These are called right-angled triangles.
An ancient Greek called Pythagoras discovered something
special about them: If you draw squares on each side,
the area of the two small squares adds up to the area
of the big square.
It doesn't just work for squares, it works for any shape...
even elephants!

Sierpinski's Triangle

Triangles within triangles within triangles
within triangles.
..and all of them are self-similar!

This is fractal!

To draw one click here:

Make a 3D model:

Pascal's Triangle

This interesting triangle is made by arranging numbers.
Do you see the pattern?
Try filling in the missing numbers.

To see what Pascal's Triangle has to do with
Sierpinski's Triangle visit this site.

Sierpinski and Fractal Art

Fractal artists use maths to draw a self-similar fractal shape and, using a special computer programme,
they repeat, spin, twist, stretch, colour, flip and rotate the shape with some amazing results:

Google Fractal Art for hundreds more images.
Zoom in closer and closer and closer and closer on fractal images!

Fractals occur in nature.

Cauliflowers, ferns and trees are good examples.
The pieces broken off a cauliflower head or a
fernfrond are tiny-sized copies of the whole.

The Penrose Triangle and Optical Illusions


Pick up a template to build your own from the Library.
See more optical illusions here.
Can you see the two impossible triangles in
this famous picture by Dutch printmaker
M.C. Escher (1898-1972)?
Hint: Follow the water down the waterfall
and check the height of the two towers.

Triangles and Art: The Vanishing Point

The vanishing point is a special trick used by artists to make their pictures look as if they are going back
into the distance.This is called perspective.

Draw your name in 3D:
Visit Mark Kestler's 3D Drawing site

Mysterious Triangles


The Bermuda Triangle

Also known as the Devil's Triangle, this area in the
western Atlantic Ocean accounts for the mysterious
disappearance of more than 50 ships and 20 airplanes.

Begin your investigation here.


The Black Triangles

"The object I saw was on the opposite side of the highway,
hovering perfectly still about 20ft above the tree-line...
The object itself was an equilateral triangle. At each point
on the underside, was an almost painfully bright blue-white
light. The object was perfectly still and made no sound that
I could hear" - Maine, USA, Feb 1, 2007

Triangles to find your way:

Using your watch:

Point the 12 on your watch towards
the sun. Imagine a line halfway between
the 12 and the hour hand.
This points North.
Using the stars:

The point at which the 2 imaginary lines meet is in a very
dark part of the sky. This point is South.

Making Curves from Triangles: String Art


Curves from straight lines?

Try it!

Jigsaw together some Egyptian vanishing points: