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Phi

My Science Tattoo: Why I did it, and what it means?

I got my tattoo yesterday, here is how it looks like. When a close friend, co-worker, or family looks at it for a minute, I get two immediate reactions:

1. That's a badass tattoo! But what is it? What it means?
2. Why did you do it? If you change your mind later on what you inked then [blablabla]...

I've always liked tattoos and for some time wanted to get something done that was truly meaningful to me.  I was inspired and got my last bit of courage from the Science Tattoo Emporium Discover Magazine, and decided to materialize it.

Here is what I incorporated in the tattoo and why:

Pi (Π)

Why?: There are the three math constants that blow everybody's mind once they realize how closely connected they are to the universe. They are Pi (Π), Euler(e), and Phi(φ). For my tattoo I decided to go with Pi, since is a universally known constant that doesn't require much introduction, yet is a totally badass one. Here's why:

1. It's one of the oldest known constants in mathematics. It dates back to 2589–2566 BC, when the Egyptians built the Great Pyramid of Giza, whose ratio between the volume and height is exactly 2Π.
2. Pi is found everywhere we see a circle shape, since you calculate Pi by dividing the circle's circumference by its diameter (Π=C/d). Many people learn this by memory in school, but never truly get to understand what it means, or even how to interpret what Π represents in the context of a circle. The circumference of a circle is slightly more than 3 times its diameter, and number is what Π represents. Wikipedia has a good animation of Pi 'unrolled'
3. 4. Pi is both irrational and transcendental, and passes all tests for normality and statistical randomness. These properties make it the only known constant with universal distribution of its digits that cannot be represented by the fraction of any two numbers, or polynomial with rational coefficients.
5. Pi is part of the most beautiful mathematical equation of all time: Euler's identity
6. 7. Pi is heavily used in formulas from other branches of science, such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics and electromagnetism.

Carbon Atom

Why?: Carbon element is present in all forms of life. It the most abundant element by mass on the human body, only after Oxygen. Every organic compound is takes form, mass and strength thanks to carbon bonds, making carbon the chemical foundation of all known life.

Fibonacci Tiling

Why?: Fibonacci tiling is the composition of squares whose sides are successive Fibonacci numbers in length (1,1,2,3,5,8, etc). The series F(n) = F(n-1) + F(n-2) is a mysterious one in the world of mathematics. Its exemplar simplicity makes it easy to be understood by almost every body, yet it's found in the most complex settings in science. Here are a few that will blow your mind:

1. The Fibonacci numbers are also an example of a complete sequence. This means that every positive integer can be written as a sum of Fibonacci numbers, where any one number is used once at most.
2. Found in the sum of shallow diagonals in the Pascal Triangle
3. In numbers represented on base 2, or binary, they are spotted quite often. The samples below and the fact that computer science and electrical engineering use the binary system more than I can count every second, makes this sequence far more interesting  and mysterious to me. Check this out:
• The number of binary strings of length n without an even number of consecutive zeroes or ones is  twice  Fn.
• The number of binary strings of length n without an odd number of consecutive ones is  Fn+1.
• Also, the number of binary strings of length n without consecutive ones (1) is Fn+2.
4. The Fibonacci cube is an undirected graph with a Fibonacci number of nodes that has been proposed as a network topology for parallel computing.
5. In music, Fibonacci numbers are used to determine tunings, and, as in visual art, also to determine the length or size of content in the formal elements.

Golden Ratio (φ)

Why?: The Golden Ratio is yet another mystical mathematical rarity. Two numbers {a,b} are in the golden ratio, when the sum of the quantities divided by the larger of the two is equals to the larger divided by the smaller.

1. With {a,b}, with a>b; {a,b} are in the golden ratio <=> ((a+b)/a) = (a/b)
2. To make it even cooler, it turns out that it doesn't matter what numbers a and b are, if they are in the golden ratio => a/b = φ = "Phi", a mathematical constant calculated by the equation (1+√5)/2, and dating back to Plato's time.
3. Mathematicians throughout history have obsessed with this constant, including: Phidias, Plato, Euclid, Fibonacci, Pacioli (coining it the "divine proportion"), Da Vinci, Kepler and Ohm.
4. Fibonacci series have a close relation to the Golden Ratio, so much so, that Kepler observed how consecutive numbers in the Fibonacci series converge to the Golden Ratio. This is both sick and awesome, like some sort of mind game the universe is playing on us:
5. 6. In art, it is a proportion that dictates aesthetical pleasures to the human eye. It is found in master pieces such as Leonardo Da Vinci's "Mona Lisa" and Salvador Dali's "Leda Atomica"
7. In Nature, the Golden Spiral (one on the center of the tattoo) is found in the shapes of many living organisms, such as:
1. The arrangement of branches along the stems of plants and the veins in leaves;
2. The skeletons and adjacent bone lengths in animals;
3. The proportions of chemical compounds and the geometry of crystals
4. Almost all human body proportions between adjacent organs, organ systems, bones, and body parts exist in complete harmony following the Golden Ratio.
5. The groves of the human DNA's double helix.
6. The human perception of beauty is based on how closed our facial expressions align with the Golden Ratio.
8. From cloud formation, to river networks, to craters, lighting bolts and coast lines, the Golden Ratio has a recurring presence.
9. There are too many manifestations of the Golden Ratio in science to mention here; but one of the most interesting ones is in chaos theory and the fractal sets.
10. With all the above, you feel there is something magical, mysterious and universal about Phi and the Golden Ratio, that makes it a special science jewel.

Silicon

Why?: Silicon is a chemical element with atomic number 14, that makes about 28% of Earth's crust. Is also one of the most used materials in the production of semiconductors and integrated circuits used in computers every day. That's where the "Silicon Valley" name comes from. The reasons for choosing this element as part of the tattoo are obvious to those that know me over the years. I'm the ultimate nerd, and I'll be wearing those circuits in my arm with proud. I think is pretty safe to say these science elements will not change anytime soon, so my tattoo will remain meaningful to me an the world in the foreseeable future ;)

I'm super happy how it turned out... and I'll be sporting my science tattoo for the rest of my life with pride.

There is strong, and then, there is nerd-strong! :P