What is a Gnomon?

The gnomon, or a stick in the ground, was the most sophisticated mathematical instrument to humankind for thousands of years.

Gnomon

 

The Gnomon And The Calendar

A gnomon is a vertical pole in the ground, with the light of the sun casting its shadow onto the ground at a right angle to the gnomon.

By observing and documenting the shadow length for hundreds and even thousands of years, one could determine that:

1.  the longest shadow length of a solar year would mark the winter solstice 

2.  the shortest shadow length of the year would correspond to the summer solstice. 
Spring and Autumn equinox would fall in the center of the two solstices, so the gnomon was the calendar maker.  

The relationship of the shadow to the gnomon is the right angle also known as the Pythagorean Theorem and is consdidered the most important math formula to humankind. 

The gnomon, right angle, carpenter's square, and Lo Shu are all related to the concepts of Time and Space because of the correspondence of the Calendar and the Pythagorean triplets of numbers.

This mathematical relationship or formula is related to man evolving from a nomadic existence to a sedentary one.  A nomadic existence with no permanent dwellings meant man was on the move in a hunter and gatherer lifestyle and lived in natural shelters such as caves or temporary and portable shelters such as tents.

Applying the math of the gnomon/right angle triangle theorem helped man to evolve from the nomadic lifestyle to a sedentary lifestyle based on agriculture and permanent dwellings. Mathematics plays a great role in the evolution of man and when used with intention can lead to a society's advancement in the arts of music, astronomy, astrology, agriculture, architecture, and other fields.

 

 How to use a gnomon

1.  Longest observed shadow corresponds to winter soltice, the first day of the year.

2.  Shortest observed shadow corresponds to summer solstice. marks one half of a solar cycle.

3.  The half way point between these two dates will mark spring and winter equinox.

4.  There are 91.328 days or six fortnights to a season.

 

One unit of calendar measurement of the solar cycle  was the fortnight.  One fortnight was equal to 15.218 days.  This would be equal to six fortnights to a season and twenty-four fortnightly periods to a year.

Each fortnnightly period was the equivalent to a 150  movement  of the Sun along the longitudinal elliptic.

Math’s Greatest Instrument, The Gnomon, and the Greatest Experiment

One of the cleverest experiments was performed by Eratosthenes more than 200 years before Christ.

Eratosthenes proved that the earth was round and came within fractions of estimating the Earth’s circumference by using the shadow length of two gnomons that were located 800 km apart.

In Syene it was known that at the summer solstice the shadows of gnomons would disappear, demonstrating that the sun was directly overhead.  To prove this, Eratosthenes traveled to Syene to look down a well at precisely summer solstice and he could clearly see the water at the bottom with no shadows cast on the walls of the well.  

However, in Alexandria, which was 800 km away, there was a definite gnomon shadow at precisely summer solstice.  Syene was close enough to the Tropic of Cancer that there is no gnomon shadow because the rays of the sun were exactly 90 degrees to the ground, whereas in Alexandria the sun’s rays were at 83 degrees to the ground and thus a shadow was cast. 

This proved that the Earth was round.  In addition, Eratosthenes was able to use the proportion of 7/360 and the distance (800 km) between this angular difference of the suns parallel rays to the ground at Syene and Alexandria to calculate the Earth’s circumference. 

Observing and documenting the shadow of the gnomon for thousands of years led to a functional calendar, proved that the Earth was round, and determined the Earth’s circumference.