5.26.2010

For this 5'1" Arc-Swallowtail, I wanted to find what might be the closest thing to "sacred geometry" in this design.  So I first built the foundation dimensions of the tail with an equilateral triangle which defines the width of the tail at its widest point.  Since all sides of this equiangular triangle are equal in length, this length also defines the radius of the circle which transcribes the arctail. The length of the equilateral triangle (and the radius of the circle) is 12".

The foam removed for the swallowtail is an isosceles triangle whose vertex is one half the angle of the equilateral or equiangular triangle, one half of 60º, which is 30º.  The length of the base of this isosceles triangle is one half its height, in this case 4" wide and 8" deep.

There is a relationship between the numbers here: 1, 2, 4, 8...

From Wikipedia:


"In mathematics1 + 2 + 4 + 8 + … is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2.
\sum_{k=0}^{n} 2^k.
As a series of real numbers it diverges to infinity, so in the usual sense it has no sum. In a much broader sense, the series is associated with another value besides ∞, namely -1.
In the history and education of mathematics1 + 2 + 4 + 8 + … is the canonical example of a divergent geometric series with positive terms. Many results and arguments pertaining to the series have analogies with other examples such as 2 + 6 + 18 + 54 + …."

These relationships are proportions which can be used to scale the design up or down depending on the length of the board.

7 comments:

moon mom said...

You really should stop eating Zooey's Science Diet.

chum said...

fibonacci

m.caro said...

yo chum---

The Fibonacci sequence is a series of numbers where each number is the sum of the two previous numbers. For example the sequence starts with 0 and 1, then 1+2=3, 2+3=5, 3+5=8, 5+8= 13, 8+13= your mom....and so on and so forth. it looks like this:

0, 1, 2, 3, 5, 8, 13, 21, 34, 56...to infinity.

If you graphed these numbers on a grid, they would define the "Golden Spiral" and the ratio of adjacent numbers would get closer to the irrational number Phi, which is the "Golden Ratio."

These ratios define most everything in nature, from the shape of the spiral going down your toilet to the shape of our galaxy. It can be used to make board templates as well as to calculate trajectories through space.

Now stick that in your solar-gravity-bong and smoke it :)

chum said...

"It's not difficult to find examples of most any pattern or mathematical relation you want. Then some people make the mistake of supposing this reveals some mystical governing principle in nature. This is reinforced by ignoring equally important cases that don't fit the pattern. If the fit isn't very good, approximate or fudge the numbers. If some things remain that ought to fit but don't, just rationalize a reason why they are 'special cases'. Folks addicted to mystical mathematics are really motivated by a belief that there's something 'magical' about certain combinations of numbers. They are obsessive pattern seekers. Pattern recognition can be a useful trait, if not carried to the point of believing that every perceived pattern represents something profound or mystical".

puff.

frank said...

sacred geometry is a fascinating subject, like you said, the proportions of an egg, the growth pattern of a nautilus shell, and so on - it also manifests itself as the proportions of the human figure related to man made creations (architecture, art, etc...) and certainly must apply to surfboards! - check out the documentary "Chartres Cathedral, a sacred geometry"

btw, your sticks really look cool, I dig them!

mastsurfboards.com said...

wow! can we cover free will vs. predestination next?

Nice shape, Manny

This is not Ian said...

nice tail :)?