Interesting+Triangles

=Interesting triangles=


 * [[image:P1070462-1.JPG width="251" height="285"]] || ===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!** ||

Triangles within triangles within triangles within triangles. ..and all of them are self-similar!
 * ===Sierpinski's Triangle===


 * This is fractal!**

To draw one **[|click here:]**

Make a **[|3D model:]** || || This interesting triangle is made by arranging numbers. Do you see the pattern? Try filling in the missing numbers.
 * ===Pascal's Triangle===

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.
 * [[image:de-colores-wallpaper.jpg width="237" height="207"]] || [[image:doublespiral_mandelbrot_center.jpg width="262" height="213"]] ||
 * [[image:alien-waves-wallpaper.jpg width="244" height="212"]] || [[image:lighted-path-wallpaper.jpg width="265" height="215"]] ||
 * [| Zoom in closer]** and closer and closer and closer on fractal images!

Cauliflowers, ferns and trees are good examples. The pieces broken off a cauliflower head or a fernfrond are tiny-sized copies of the whole. || ||
 * ===Fractals occur in nature.===

The Penrose Triangle and Optical Illusions

 * [[image:penrose-impossible-triangle.jpg width="297" height="275"]]

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)? and check the height of the two towers. ||
 * Hint:** Follow the water down the waterfall

Triangles and Art: The Vanishing Point
into the distance.This is called perspective.
 * [|The vanishing point]** is a special trick used by artists to make their pictures look as if they are going back


 * [[image:vanishing_points.jpg width="276" height="200"]] || [[image:linear.jpg width="306" height="193"]] ||
 * [[image:persp6.gif width="211" height="160"]]
 * [| Draw your name] in 3D:** || [[image:studio2.jpg width="270" height="209"]]
 * Visit Mark Kestler's [|3D Drawing site]** ||

Mysterious Triangles

 * [[image:bmd_trg2.jpg width="279" height="275"]]

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.] ||


 * [[image:Blacktriangle.jpg width="333" height="269"]]

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
 * [|More...]** ||

Triangles to find your way:

 * [[image:fig1-5.gif width="193" height="186"]]
 * 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

 * [[image:string0.gif]] || ===Curves from straight lines?===

[|Try it!]
||

Jigsaw together some Egyptian vanishing points:
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