## Friday, January 27, 2012

### sacred geometry

from phi to Fibonacci

It all started with a single point. A vertex.

Then two vertices were joined by a line. A line segment.

Then three line segments formed a polygon with three sides. Triangle.

Joined by a fourth line, the polygon became a quadrilateral. Trapezoid. Parallelogram. Square.

A fifth line segment formed the pentagon. Pentagram. Pentacle. Star.

Moving through the seventh grade geometry was about the evolution of shape and its properties as it transformed from a single point to a pentagram. Much like the evolution of the universe from a single particle to the infinite stars.

On a human level, the sacred geometry was discovered in the ebb and flow of the Nile River. The ancient Egyptians used the magical 12-knotted rope to plot perfect right angles for crop fields whose boundaries were washed away with the seasonal floods of the Nile. They discovered the aesthetic quality of the golden ratio to design the Great Pyramids. Centuries later, Thales of Miletus establishes theorems to formalize geometry.

On a more personal level, Leonardo Pisano aka Fibonacci was fascinated - no, obsessed - with numbers all around him. Unlike his up and coming Renaissance counterparts who found beauty through paint and marble, he found beauty in nature's numbers. 0, 1, 1, 2, 3, 5, 8, 13... The same numbers seemed to appear everywhere. Mother Nature revealed herself to Fibonacci - it was the growth pattern of the universe.

The universe, indeed, for the Fibonacci numbers even reflected the approximate lengths of the lines of a pentagram. Each line, in relation to the next longest or shortest line, was close to the ratio of 1.618 to 1, the golden ratio, phi.

The seventh grade students discovered the golden ratio in the star. But they did not have to look to the stars to find it, for in their own fingertips, they held the golden ratio in the lenghts of their bones. The point was driven home once again, we are connected to the universe.

Our study of geometry took us to the introduction of measuring volume in cubes, cylinders, and spheres. In art, we continued to refine our skills in manipulating light and shadow. With an advanced technique of drawing black and white on blue paper, we got some magnificent effects of contrast and realism in the study of a hand holding a cube.

## Saturday, January 14, 2012

### star cross'd

When one thinks of the Renaissance, usually one pictures Leonardo da Vinci, Michelangelo, or the Medicis. But if you travel westward from the Italian countryside, cross the vast western European taiga forests, and swim to the British Isles, one encounters the greatness of the English Renaissance. Here, it is not about the explosion of painting and sculpture, instead, the Elizabethan theater. And one immediately recalls the great wordsmith of 16th century England, William Shakespeare.

Renaissance history for the seventh graders of Davis Waldorf would not be complete without the performance of a Shakespearean play. However, perhaps in the spirit of creativity, and in a very conscious effort to give a balanced amount of lines for each of my students, I wrote a play, which incorporated passages from Shakespeare's plays, epic poems, and sonnets.

The play is titled Star Cross'd. It takes us on a journey from Shakespeare's birthplace of Stratford-upon-Avon to the Globe Theater in London. What had interested me as I imagined the plot of Star Cross'd was how Shakespeare got his start, and what inspired him. His life during the time of Queen Elizabeth I included many people that were as interesting as his fictional characters, so I decided to include some of them in our play. And though while historically they existed, I took creative license in their interactions with Shakepseare.

If love is at the heart of the writer's soul, then it was Anne Hathaway, Shakespeare's wife, who was his muse. When Shakespeare leaves Stratford, he arrives in London at the Master of Revels office where he meets the Burbages, financiers and actors in the Chamberlain's Men. The Master of the Revels is the Queen's censor, and with Shakespeare's wordsmithing prowess, the Burbages ask Shakespeare to join them as their playwright.

The play jumps a few years and Shakespeare is invited as the guest of honor of the Queen and her Royal Court. Here, he meets Sir Walter Raleigh and Bess Morton (Elizabeth Throgmorton). I discovered that Morton was secretly in love with Raleigh and the two eventually married each other. I decided to use their secret love affair as the vehicle that inspires Shakespeare to write his play Romeo and Juliet. So the second half of our play is a "play within a play," as the Chamberlain's Men perform Rome and Juliet (excerts from the play) for the Queen and the Royal Court to convince Bess Morton to follow her heart.

Here is an excerpt of our play, where Shakespeare is quietly talking to Bess Morton:

BESS MORTON
Oh, Mr. Shakespeare, I hope I did not offend thee
With an amateur’s recitation of your epic poem.

SHAKESPEARE
No, not at all! I express the opposite, gentle lady.
Words are just words without heart. And your heart
Sings of one truly in love. And dare I presume, a love

BESS MORTON
Sir, you are gifted in knowing the human soul.
It is no wonder the characters in your plays speak
With genuine emotion.
I am in love, but I must not act upon my heart’s call.
As Lady to the Queen’s Privy Chamber, I am
To serve only Her Majesty.
I am forbidden to fall in love.

SHAKESPEARE
Forbidden to fall in love?!
Can a rose be forbidden to bloom in beauty?
Can the wind be ordered to hold sway its might?
Can the sun be estopped from slicing the summer sky
With it glorious rays of light and heat!!

BESS MORTON
The Queen cannot ever know, else I draw her rage.
Or worse, I become a prisoner of the Tower.

SHAKESPEARE
Oh dear Lady Bess, I am reminded of what my
Wife Anne tells me:
Love looks upon tempests and is never shaken.
We were young, foolish perhaps, but impassioned
By the unwavering truth of love.
A Queen’s temper cannot temper love.

BESS MORTON
You are asking me to disobey the wishes of my Queen.

SHAKESPEARE