Yale Law Journal (via moralanarchism)
I wrote the right to jury nullification on one of my answers when I was called in for jury duty a couple of years back. Needless to say, my name wasn’t even called for jury selection. lol
Things to know about Fibonacci and his Numbers -(by request)
Leonardo Pisano Bigollo (known as Fibonacci, and also Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci) —was an Italian mathematician, considered by some “the most talented Western mathematician of the Middle Ages.”
Fibonacci is best known for the spreading of the Hindu–Arabic numeral system which we use today in modern times - In his Liber Abaci (1202), Fibonacci introduced the modus Indorum (meaning method of the Indians), today known as Arabic numerals - which include the numbers 0 - 9 and was one of the earliest numerical systems to use zero as a place holder. The book also advocated place value in early hindu-arabic numerals.
^ modern Arabic numerals
The Fibonacci sequence
The Fibonacci numbers were introduced in his Liber Abaci which posed, and solved a problem involving the growth of a population of rabbits based on idealized assumptions.
The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci’s Liber Abaci that introduced it to the West.
the Fibonacci sequence is widely known for its interesting properties. the one you may be most familiar with is that every term is the addition of the previous two terms:
for example, the Fibonacci sequence is represented here in this famous pattern.
Your sequence begins with a square with side length of 1. Imagine this is one rabbit - if you pair one rabbit with no rabbits you will have no offspring. we then add a partner rabbit, so you have 1 and 1 paired together.
the number of offspring they produce is the sum of the previous two generation’s population, in this case because we start with only 1 and 1 rabbits we get 2 in the next generation.
at this point your sequence looks like 1,1,2,
your next population of offspring continues the same rule - the sum of the previous two populations of the rabbit generation. So in this case where X is our fourth population in the next generation (1,1,2,X). X is the sum of 1 and 2 - the previous two populations.
The Rule is Xn = Xn-1 + Xn-2
so we now have the sequence 1,1,2,3
and the 1,1,2,3,5
and the sequence can carry on to infinity:
The characteristics of the Fibonacci sequence is commonly found in sunflower seeds and seashells as well as many other forms of nature, Art and Architecture.
The Golden Ratio
The Fibonacci numbers were first expressed in terms of the Golden ratio by Daniel Bernoulli in 1724.
The Golden ratio is one of the few Famous Mathematical constants along with e, √2, and π. It is an Irrational number.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
If we continue divide a term in the Fibonacci sequence by its preceding term we eventually approach the Golden ratio designated by the Greek numeral ϕ (phi, lowercase φ):
the Golden ratio is approximated to the decimal 1.618033988
with this we can show that each Fibonacci number can be written in terms of Phi.
^ The golden ratio fits coherently with the Fibonacci pattern (where the curve is the Golden ratio and the squares are the Fibonacci numbers.)
^ Fibonacci numbers can be found in many other mathematical discoveries, as it is the one of the most naturally occurring sequences in Mathematics. Fibonacci numbers can be found in the Pascal triangle when you add the numbers diagonally.
Finding the Nth term in the Fibonacci sequence
The Formula to find the Nth term in the Fibonacci sequence can be calculated with the Golden ratio:
A number of mathematical, computing, and engineering jobs are on the list.
what doesnt kill you gives you exp points
Sachiko Kodama explores within her artwork ‘The Art and Science of Ferrofluid’ the pulsating nature of science and amorphous character of time and space based on the shape of magnetic waves…
The Japanese female artist Sachiko Kodama was born in 1970. As a child she spent a lot of time in the southernmost part of Japan. This area is rich in tropical flowers and plants, edged by the sea, and washed with warm rain. Sachiko loved art and literature from an early age, but also had a strong interest in science.
After Graduating Physics course in the Faculty of Science at Hokkaido University, in 1993, Sachiko matriculated in the Fine Arts Department at the University of Tsukuba, studying Plastic Art and Mixed Media. Then she completed Master’s and Doctoral Program in Art and Design at the University of Tsukuba. She studied Computer and Holography Art in her doctoral research.
‘Ferrofluids appear as black fluid and are made by dissolving nanoscale ferromagnetic particles in a solvent such as water or oil. They remain strongly magnetic even in a fluid condition which makes them more flexible than iron sand.’