More About Einstein

The deep connection Einstein discovered between energy and mass is expressed in the equation E=mc^2. Here E represents energy, m represents mass, and c^2 is a very large number, the square of the speed of light. Full confirmation was slow in coming. In Paris in 1933, Irene and Frederic Joliot-Curie took a photo showing the conversion of energy into mass. A quantum of light, invisible here, carries energy up from beneath. In the middle it changes into mass--two freshly created particles which curve away from each other.

Albert Einstein

Albert Einstein is perhaps the most famous scientist of this century. One of his most well-known accomplishments is the formula E=mc^2. Despite its familiarity, many people don't really understand what it means. One of Einstein's great insights was to realize that matter and energy are really different forms of the same thing. Matter can be turned into energy, and energy into matter.

More About Pascal's Triangle

Blaise Pascal was not the first man in Europe to study the binomial coefficients, and never claimed to be; indeed, both Blaise Pascal and his father Etienne had been in correspondence with Father Marin Mersenne, who published a book with a table of binomial coefficients in 1636. Many authors discussed the ideas with respect to expansions of binomials, answers to combinatorial problems and figurative numbers, numbers relating to figures such as triangles, squares, tetrahedrals and pyramids.

Where Pascal's Triangle Really Started

The so called "Pascal" triangle was known in China as early as 1261. In 1261 the triangle appears to a depth if six in Yang Hui and to a depth of eight in Zhu Shijiei in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in the eleventh century. They used it the same way we do, as a means of generating the binomial coefficients. It wasn't until the eleventh century that a method of solving quadratic and cubic equations was recorded, although they seemed to have existed since the first millennium. At this time Jia Xian generalized the square and cube root procedures to higher roots by using the array of numbers known today as the Pascal triangle and also extended and improved the method into one usable for solving polynomial equations of any degree.

Angel Investing and Teselations

An angel investor or angel (also known as a business angel or informal investor) is an affluent individual who provides money for a business start-up, usually in exchange for ownership equity. A small but increasing number of angel investors organize themselves into angel groups or angel networks to share research and pool their investment capital. Angels typically invest their own funs. Angel investing deals with money, which deals with numbers, which deals with math, because in math, you use numbers. That is how angels are mixed in with math. :)

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Another word for tessellation is a tiling. The dictionary says that the word "tessellate" means to form or arrange small squares in a checkered or Mosaic pattern. The word "tessellate" comes from the Ionic version of the Greek word "tesseres," which in English means "four." The first tilings were made from square tiles. A regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A regular tessellation means a tessellation made up of congruent regular polygons.

Angels

The angels in this picture represent math by reflection. The angels reflect across the X and Y axis and/or are upside down and flip in a different way. Reflection is when an image is produced by reflecting as by a mirror. This picture shows that with the angels. Many are reflected, rotated, or flipped showing the same image, just in a different manner.

This picture is of a tessellation. It is very pretty. There are no gaps between the angels. That is because it is a tessellation. There aren't supposed to be any gaps between the angels or other shapes used in the making of tessellations.

A Butterfly Lesson

There are many ways you can put butterflies into a math lesson, but I personally like this one the best. In this particular picture, you must solve the math problems to figure out the color. If you get them all right, you can color the picture!

Butterflies Mixed in With Math?!?

Who knew that butterflies could be used in math! Butterflies are used everyday to teach young children about the line of symetry. Kindergarten, first, and second graders use butterfly wings to learn about the math concept of symetry.

More About Fractals

In math, any of a class of complex geometric shapes that commonly have fractional dimension, is a fractal. Fractals are distict from simple figures of classical geometry. These are the square, circle, sphere, and etc. They are capable of describing many irregularly shaped objects. The term "fractal" was derived from the Latin word "fractus" which means fragmented or broken.

History Of Fractals

The mathematics behind fractals began to start in the 17th Century when mathematician and philosopher Leibniz considered recursive self-similarity. It was not until 1872 that a function appeared whose graph would be considered a fractal today. This is when Karl Weierstrass gave an example of a function with the non-intuitive property of being everywhere continuous but nowhere differentiable.