The average kinetic energy of the object would be kBT, and the time decay of the fluctuations would be entirely determined by the law of friction. The theory of fluctuations, he realized, would have a visible effect for an object which could move around freely. Such an object would have a velocity which is random, and would move around randomly, just like an individual atom.

-clarence

Albert Einstein was a theoretical physicist who is widely regarded as one of the most influential scientists of all time. He modified Planck’s hypothesis by stating that the lowest energy state of an oscillator is equal to 1⁄2hf, to half the energy spacing between levels.




-clarence

Pascal's Triangle II

Pascal's Triangle was originally developed by the ancient Chinese, but Blaise Pascal was the first person to discover the importance of all of the patterns it contained. He was the first one to organize all of the information and put it all together. This happened in 1653. A number in the triangle can be found by nCr (n Choose r) where n is the number of the row and r is the element in that row. The formula for nCr is: n!
--------
r!(n-r)!


-Lindsey

Pascal's triangle determines the coefficients which arise in binomial expansions. Pascal'striangle has many properties and contains many patterns of numbers.

-Clarence

The picture of the week is Pascal's Triangle.It is a geometric arrangement of the binomial coefficients in a triangle. It is named after mathematician Blaise Pascal.

-Clarence

Pascal's Triangle

This week picture is Pascal's Triangle. It is a geometric arrangement of the binomial coefficients in a triangle. This is how the construction of the triangle works. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number directly above and to the left with the number directly above and to the right to find the new value. For example, the first number in the first row is 0 + 1 = 1, whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row. Pascal's Triangle shows up is in probability, where it can be used to find combination.

-Lindsey

The pascals triangle was the key to determine the coefficents for binomial factoring. Another good use for the triangle is in the calculation of combinations.


Austin H.

This weeks picture is Pascals triangle. Even though Blaise Pascal wasn't the first one to use these numbers, he was the first to fully organize them into a triangle. The year was 1653.

Austin H.

Angels II

Another reason why this picture has to do with math is because it has reflections of the objects in the picture. Tessellations are seen throughout art history, from ancient architecture to modern art. A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons.
Example of a tessellation-
Lindsey

Angels I

This weeks picture is angels and demons. The picture has to do with tessellations. A tessllation is a shape that is repeated over and over again covering a plane without any gaps or overlaps. Another word for a tessellation is a tiling. The first tilings were made from square tiles.

Lindsey

A tessellation with congruent tiles are called monohendral tiling. In the 1970s Michael Hirschhorn created Hirschhorn tiling. The unit tile of Hirschorn tiling is an irregular pentagon

Austin H.

This weeks amazing picture is a tessellation. A tessellation is made up of polygons that are congruent. There is only 3 true tessellations. They are made out of equalateral triangles, squares, or hexagons. Semiregular tessellations are made up of a variety of polygons.

Austin H.

A regular tessellation means a tessellation made up of congruent regular polygons. Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons. Since the regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees.

-Clarence

This weeks picture of the week is a Tessellation. Tessellations created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Another word for a tessellation is a tilling.

-Clarence

Butterflies feed on nectar from flowers. They migrate over long distances. They have four wings with tiny scales.

-Clarence

Butterflies have a line of symmetry and they are all different.







- Clarence

Each butterfly has something different on them. They are like snowflakes.

Austin Hisel

Picture of the Week

The wings are symmetrical on each side.

austin hisel

Butterflies II

Some examples of some butterlfies are the Painted Lady Butterlfy, Peacock Butterfly, Karner Blue Butterfly, and the Southern Dogface Butterfly. Butterflies can see red, green, and yellow. Butterflies range in size from 1/8 inch to almost 12 inches. There are about 24,000 species of butterflies. The top butterfly flight speed is 12 miles per hour. Examples:










-Lindsey

Butterflies!!

This weeks picture is butterflies!!! One reason why butterflies have to do with math is because they have a line of symmetry. The scientific name of a butterfly is Lepidoptera. Antarctica is the only continent on which no Lepidoptera have been found. The Goliath Birdwing Butterfly, American Snout Butterlfy, and Blue Morpho Butterfly are some different types of butterflies. Examples:








-Lindsey

There are four common techniques for generating fractals. Escape-time fractals, Iterated function systems, Random fractals, Strange attractors are those four techniques.

Fractals II

In the 17th century, Gottfried Leibniz discovered the mathematics behind fractals. It wasn't until 1872 that Karl Weierstrass gave an example of a function that would today be considered a fractal. Some more of the applications are digital sundial, seismology, signal and image compression, generation of various art forms, and creation of digital photographic enlargements. Here are a few more examples:

-Lindsey

Fractals 2

You can apply these into a lot of things. Heres a list of them: Technical analysis of price series, Digital sundials, Seismology, T-shirts, etc.

There are 3 types of self-similarity in fractals.
Exact self-similarity
Quasi-self-similarity
Statistical self-similarity

Austin Hisel

Fractals 1

Gottfried Lebiniz discovered the fractal in the 17th century. He did this when he considered recursive self similarity. He truly made a mistake though.


Austin Hisel

Fractals

This weeks picture is a fractal. A fractal is a rough or fragmented geometric shape. That is why it has to do with math. This is another example of a fractal. Classification of histopathology slides in medicine, Computer and video game design, especially computer graphics for organic environments and as part of procedural generation, and T-shirts and other fashion are some of the applications.

- Lindsey

Fractals

This weeks picture is of a Fractal. The reason it as to do with math is because it is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole.

- Clarence