Zac - Pascal's Triangle

This is Blaise Pascal's originial version of the triangle. Pascal had developed many different arrangements of it, but this is where it started. The numbers originally arose from Hindu studies.

Lizzie - Pascal's Triangle

Each row is an arrangement of integers. You add the numbers above to get the number below. So the first blank you would 1 + 1 so you get 2. The second blank you add 2 + 1 and get 3, and so on. The remaining numbers will go 3, 4, 6, 4.

Brittany - Pascal's Triangle

This is the first rows of Pascal's triangle. The first row is the zero row. Each row starts and ends with 1.

PASCAL'S TRIANGLE

BRITTANY:
Pascal's triangle is an arrangement of the bionamial coefficients in a triangle.
It is named after Blaise Pascal, although other mathematicians studied it way before him.

LIZZIE:
The rows of Pascal's triangle are conventionally enumerated starting with 0.
The numbers in each row are usually staggered relative to the numbers in adjacent rows.

ZAC:
The set of numbers that form Pascal's triangle were well known before Pascal.
Pascal was the first to organize all the information together.

Zac - Tessellation

This picture is repeating parrallelograms. It is tiled so that it doesn't have any spaces between each one. The colors make it pretty!

Lizzie - Tessellation

This is a picture of pavement and its unique pattern keeps repeating itself. It doesn't overlap and it doesn't have gaps.

Brittany - Tessellations

A honeycomb is a mass of hexagonal wax cells. It is the same pattern over and over again. Therefore making it a tessellation.

TESSELLATIONS

BRITTANY:
A tessellation is a collection of plane figures that fills the plane with no overlaps or gaps.
Tessellations are seen throughout art history, from anciet architecture to modern art.

LIZZIE:
A tessellation is a repeating picture but turned differnt directions to fit together.
The word "tessella" means "small square."

ZAC:
Only 3 regualar tessellations exist: those made up of equilateral triangles, squares, or hexagons.
A semiregualar tessellation is made up of a variety of regualar polygons.

Zac - Symmetry

This is a great example of symmetry. You can fold the picture in half vertically and it will the same on both sides. This picture only has one line of symmetry.

Lizzie - Symmetry

The petals on the flower are symmetrical because they are the same no matter which way you divide them. Symmetry makes the flower look beautiful and we like beautiful flowers.

Brittany - Symmetry

This star has five lines of symmetry. You can cut it several differen ways and it will be the same. I like stars, especially purple ones as shown.

Symmetry

BRITTANY:
It's a thing of proportionality and balance.
It reflects beauty and perfection.

LIZZIE:
It's a pattern of self-similarity.
It can be proved by geometry and physics.

ZAC:
There are several kinds of symmetry, such as: reflection, rotational, and translational.
The most familiar type is geometrical symmetry.

Zac-Fractal

ZAC!!!!!

Koch Star: It is one of the earliest fractal curves that has been described. It has an infinite length because it goes on forever. It is based on the Koch curve.

Liz-Fractal

LIZZIE!!!!!

Menger Sponge: This is a fractal curve. It was first described by Karl Menger. It is a closed set.

Brit-Fractal

BRITTANY!!!!!

Sierpinski triangle: It was orginally constructed as a curve. It's one of the basic examples of a fractal. It was named after Polish mathematician Waclaw Sierpinski.

FRACTALS

BRITTANY:

It was coined by Benoit Mandelbrot in 1975.

Comes from the meaning "broken" or "fractured."

LIZZIE:

They are often considered infinitely complex.

Fractals came about in the 17th century by a man who mistakenly came up with it.

ZAC:

We use fractals for t-shirt and fashion and also for generations of new music and various art forms.

Fractals are easily found in nature, such as clouds.