The harmony and coherency of the visual world is based on relationships and devices such as ratios. The task of creating an integral balance to the experience of life is daunting but demanded of those that pursue art and design. Mathematics is the language that unifies us all under the auspices of Nature and **proportion** answers the divine.

As a designer, a rose bud, an apple, a tortoise shell, a spider web, a pine cone, a ram’s horn, crystals, corn on the cob, a sea shell, a flower, all represent Nature . The simple geometric shapes are ordered through numbering devices to create precise proportional systems.

**The nature of proportion!**

## Activity 1 – Proportion In Nature

Select any one of Nature’s proportional examples if you can locate them firsthand. Then begin to analyze the shape and volume in 2-D and 3-D drawings. Measure the dimensions and create scale drawings so you can begin to create the numbers found within the design of the objects. When you have uncovered the mathematics found in the natural, create a final presentation on 11 x 17 paper to display your findings. Then, take a look at these **digital sculptures**, called *aniforms*, based on nature’s proportions found in pine cones and sunflower seed arrangements.

## Activity 2 – Golden Mean

The golden mean is a proportion found in nature, in the human body and in architecture of key buildings throughout the ages. The golden proportion is most commonly known as 1:1.618. Ancients discovered it as the most visually pleasing of all proportions. In fact, its emergence in Swiss Design is thought to have originated in Africa. The golden ratio, named so because its dimensions are thought to represent great beauty, is very simple to construct. Find a compass, ruler, protractor and a pencil. Next, draw a square and divide it in half with a vertical line. Place the pointed end of your compass at the point where the center line meets the base of the square and put the pencil end of your compass at the upper right, or left, hand corner. Draw an arc downward to a line that extends past the base line of your square. The point of this intersection will show you the outside edge of your golden rectangle. Explore the **Golden Mean**.

**Go for the Gold!**

## Activity 3 – Proportion and You!

Vitruvius, in his Ten Books on Architecture, writes about the proportions of the human body. In fact, his descriptions of a human figure circumscribed in a circle and a square were later drawn by Leonardo Da Vinci and are known as the Renaissance Man. Reference this resource: http://goldennumber.net/life.htm. Photograph yourself or a friend as a Renaissance person! For this exercise you will need two pictures: your figure from the front standing up, feet together, with arms outstretched from your shoulders; and feet apart, making an “x” with your outstretched arms. Print your photographs and cut out the two figures.

**figure 1**

Trace the outline of your first figure on a new piece of paper. Next, paste your x figure over the traced outline. Using your belly button as a center, draw a circle that is tangent to your outstretched fingers and toes. Do you fit into a circle? Then draw a square across the top of your head with sides down from your outstretched arms and a base across your traced feet.

**Do you fit into a circle and a square?!!!**

## Activity 4 – Part to the Whole

**figure 2**

Place your figure on a new sheet of paper. Using your standing up straight figure, draw six vertical parallel lines equal to your height. Label one line feet, the next line label head, the next forearm, the next hand (wrist to longest finger), the next chest to top of head. Now measure your head, from your hairline to your chin; measure the length of your foot; measure the length of your forearm from your elbow to your tip of your wrist; and measure your hand from the wrist to your longest finger. From the middle of your chest to the top of your head should be a fourth of your height as should the length of your forearm. Your head should be 1/10th of your height. Your forearm should be ¼th of your height. Your foot should measure 1/6th of your height. Are you proportioned?!!!

(Note: everyone has different proportions between the parts of the body; these proportions were considered by Vitruvius as ideal.)

Next, try label your body proportion diagram with using the **Golden Ration Typography Calculator**.

## Review

- Why is proportion important?
- What is a ratio?
- What is the ratio of the golden section?
- Where is the golden section found?
- Why did we use a compass to make our golden section drawing?

## Explore

- Architecture and the Golden Mean
- Fibonacci Numbers and the Golden Section in Architecture, Art, and Music
- Flowers and Fibonacci
- Golden Mean
- Golden Ratio Typography
- Golden Section
- Leonardo Series Drawings byAnthony Panzera
- Math in Art The Golden Mean
- Math is Fun Proportion
- NSTA Science & Art of Proportionality
- PBS Ration, Proportion & Variable Game
- Pinecones and Fibonacci Series
- Proportions of the Human Face
- Rafael Araujo Golden Mean Diagrams
- Ratios & Proportion in Chemistry
- Size Wise Lesson Proportion
- Teaching Scale & Proportion in Art
- TEDed Da Vinci's Vitruvian Man of Math
- Unfolding the Golden Rectangle
- Vegetables and Fruits
- Video Aniforms, Digital Sculptures
- Video Leonardo's Universe: Fibonacci and Golden Mean
- Video Teaching Channel: Figure Drawing
- Video The Golden Mean
- Vitruvian Man (Stanford History)
- Vitruvian Man(Wikipedia)