Are You Perfect?

Writing Prompt:

What do you consider perfect?

Essential Questions:

∆ Why do certain shapes seem more appealing than others?

∆ Have you ever wondered how similar you are to your favorite musician, actor, athlete, or other important figure?

∆ How can mathematics create beauty?

∆ What is the common element in many of the things that we find beautiful.

By Shannon Roberson

Using Mathematics to Determine Beauty:

Ratios, Proportions, and Similarity What this means is that if you divide a line into two

segments, the ratio of the larger of the sections in relation to the entire segment, is equal to the ration of the smaller section, to the longer section. Or, if you were to look at the above line, and create 2 segments within it according to the golden ratio, the total length "a+b", is proportional to segment "a" in the same way that "a" is proportional to the shorter segment, "b". In other words...

"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." ~Euclid

What is the "Golden Ratio"?

According to mathematicians as far back as the ancient Greeks and Egyptians, the element of perfection is a

ratio.The Greek mathematician Euclid defined the golden ratio over two thousand years ago, in 300 BC, while

working with ratios present in geographic figures. It is a proportion used to describe two things, mathematically

similar. The Golden Ratio is known by many other names, such as the golden mean, the divine proportion, or the

golden proportion. It is represented by the Greek letter Phi (φ), and is an irrational mathematical constant

approximately equal to 1.6180339887.

Phi is a number that has been discovered in many places, such as art, architectures, humans, and plants. It may hold the key

to understanding perfection.

How does the “Golden Ratio” appear in the human body?

What are the applications of the "Golden Ratio" in Architecture? What are the applications of the

"Golden Ratio" in Art? How does the "Golden Ratio"

appear in the nature?

Golden Ratio TimelinePhidias (490–430 BC) made the Parthenon statues.

Plato (427–347 BC), describes five possible regular solids , which are related to the golden ratio.Euclid (c. 325–c. 265 BC), gave the first recorded definition of the golden ratio.Fibonacci (1170–1250) mentioned the numerical series, the ratio of sequential elements of the Fibonacci sequence approaches the golden ratio asymptotically. Luca Pacioli (1445–1517) defines the golden ratio as the "divine proportion." Johannes Kepler (1571–1630) proves that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers.Charles Bonnet (1720–1793) points out that in the spiral phyllotaxis of plants going clockwise and counter-clockwise were frequently two successive Fibonacci series. Martin Ohm (1792–1872) is believed to be the first to use the term goldener Schnitt (golden section) to describe this ratio, in 1835.Edouard Lucas (1842–1891) gives the numerical sequence now known as the Fibonacci sequence its present name. Mark Barr (20th century) suggests the Greek letter phi (φ), the initial letter of Greek sculptor Phidias's name, as a symbol for the golden ratio.Roger Penrose (b.1931) discovered a symmetrical pattern that uses the golden ratio in the field of aperiodic tilings, which led to new discoveries about quasicrystals.

Wikipedia

Pythagoras lived in the 500's BC He was one of the first Greek mathematical thinkers. He was interested in philosophy, music and mathematics. He proved the Pythagorean Theorem to be true, and he

helped create the Golden Ratio. Pythagoras believed that beauty was associated with the

ratio of small integers.

Beauty of the Human Body

1350 B.C. Egypt 500 B.C. Greece 164 A.D. Rome 1794 A.D.

Asian Caucasian Black

Beauty is in the eye of the beholder.

Does beauty vary by race, culture or era?

What features stand out to represent the perfect face?

Is there a pattern in what we perceive as beautiful?

This two-dimensional visual of the human face is based upon the Golden Ratio. This special number is believed to symbolize perfect natural harmony.

This mask of the human face is based on the Golden Ratio. The proportions of the length of the nose, the position of the eyes and the length of the chin, all conform to some aspect of the Golden Ratio.

Look at your fingers closely. If you measure the length of the longest finger bone, and then

the length of the finger next to it, and then divide the longer

length by the shorter one, you should get a number close to

1.168.

All parts of the human body are proportional to this number. In fact, if your face is symmetric and follows this ratio, you are often said to be of exquisite

beauty.

Different cultures and civilizations have different standards and criterion concerning the ideal of woman beauty. According to the Golden Ratio, beauty is NOT declared by one specific race,

culture or era…

Beauty in Architecture

The ParthenonThe exterior dimensions of the

Parthenon form a Golden Ratio in many of the proportions.

The Great Pyramid of GizaHalf of the base, the slant height, and the height from the vertex to the center create a right triangle. When that half of the base equal

to one, the slant height would equal to the value of Phi and the height would equal to the square

root of Phi.

Beauty in Art

A golden rectangle is simply a rectangle with dimensions that reflect the Golden Ratio.

Leonardo Da Vinci is known for his artistic representation using aspects of the Golden Ratio.

Beauty in Nature

Have you ever noticed that most flowers contain a pattern?

The number of petals on a flower is often one of the Fibonacci numbers: 3, 5, 8, 13, 21, 34 or

55?

The Golden Ratio is also a logarithmic spiral. For every 90 degree turn, the radius of the

spiral grows by a factor of the phi.

In addition to natural patterns found here on earth, the spiral pattern of the Golden Ratio

can also be seen in the pattern of our galaxy.

Would the Greeks consider you PERFECT?

Golden Number