It's Getting Hot in Here!

It's been over 90 degrees every day this week so Miles decides that he wants to take a swim. What does this have to do with math? Well, lets see!

Step 1

Miles gets out his doggy pool and measures the diameter. He finds that it is 35 inches across.

Step 2

Miles fills the pool with water.

Step 3
Make sure the water doesn't overflow! Boy, it sure is hot out here!
Step 4

Miles measures the water depth and finds out it is 4 inches deep.

Step 5

Miles calculates the volume of water in the pool.

He knows that the pool is a cylinder because it’s base is a circle with a diameter of 35 inches and it has a height of 4 inches. The pool's radius will be half of the diameter, which makes it 17.5 inches. In grad school he learned that the formula for calculating the volume of a cylinder is V=3.14*r^2*h.

So he fills in what he knows and solves for the unknown, which is volume.

V=(3.14)(17.5in)^2(4in) so the volume of the water in the pool is 3,846.5 in^3.

Good boy, Miles!

Step 6
Nothing left to do but invite some lovely ladies and go for a swim!




Miles is such a show-off!

Conic Sections

Here is Miles. He was a bad dog today, so he had to wear a dunce cap. His dunce cap is a cone.

Can you think of cones that you see in your everyday life?

Cones are conic sections. A conic section is a curve that is made when a plane intersects a cone. Other conic sections are circles, ellipses, hyperbola, and parabolas. You will learn more about them in geometry.

I Ching

I Ching is an early Chinese texts. While we do not know the exact date it was written, we do know it was created before Christ. It contains a lot of mathematical information using trigrams and hexagrams. Information from the I Ching is still used today. For example, four trigrams from the I Ching are used in the South Korean flag to represent heaven, earth, fire and water.

I Ching was used by the composer John Cage for composing twentieth century music. John Cage is best known for being a composer of aleatoric music; a style of music created when some elements are left to chance. When he was introduced to the I Ching in 1951 he became fascinated with its ability to create order out of chance. He used the coin method to compose “Music of Changes,” a piece for solo piano. He composed by creating a sound chart made of 64 squares. He would reference the I Ching as to which sound to use from the sound chart and then for determining other details such as the dynamics, duration and silence of the sounds. Silence was frequently employed in Cage’s compositions, as he was very interested in the “interchangeability of sound and silence.”

Did you enjoy listening to this piece of music?

If you are bored and want to read more about it, click here: I Ching

Are You Mathematically Beautiful?

It has been proposed that if the dimensions of your face coincide with the golden ratio, Phi, than you will be beautiful. The Marquardt mask is based on phi, pentagons and dedecagons. The mask can work for women of any ethnicity and from any time period. It even works on men!

You can see if your facial features fit the mask here: Marquardt Mask

Check out this site for more information: The Golden Number

Phi - The Beautiful Number

Have you heard of Phi? It is often called the golden ratio or the golden rectangle and is equal to approximately 1.618. It is used in architecture, such as the Parthenon, and you frequently see it in nature. A grad school classmate is studying the use of phi in music and has found that it occurs in "Under the Sea" from Disney's The Little Mermaid. Music is often composed so that the climax mathematically fits the golden ratio. If you listen carefully you'll hear it occur right when the blowfish blows!

Frank Lloyd Wright

Frank Lloyd Wright was an architect who strived to create a natural aesthetic in his work. His organic designs feature large flowing interiors and low horizontal lines. This photo is of Fallingwater, which is located in Pennsylvania.

Can you see math in his design?

Have you ever visited Fallingwater?

Fallingwater website