How To Play Sudoku

Enter numbers into the blank spaces so that every row, column and 3x3 box contains the numbers 1 to 9, Every Sudoku puzzle has a unique solution!

While traveling through North Africa, Fibonacci, an Italian from Pisa, discovered that the local number system of the Arabs, which uses the zero as a place holder and the numbers 0-9 found on the top of your keyboard, was far superior than the obscure combination of X's, V's and I's the Romans had invented a millennium earlier. Fibonacci brought this number system to Europe and eventually we invented Sudoku to have fun with it.

Mathematics serves us well in finding order and patterns when observing nature’s models, systems, processes and elements for inspiration to drive innovation, to borrow lessons from nature that may more effectively solve even routine problems, such as our sponsor's skin care products for acne treatment, to clear rosacea, get rid of pimples, remove acne scars and the best deep cleansing at home microdermabrasion cream..

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Mathematics, Fibonacci & Nature Inspires Skin Care

Leonardo Pisano Bigollo (c. 1170 – c. 1250), also known as Fibonacci, is best known to the modern world for the spreading of the Hindu–Arabic numeral system in Europe, primarily through the publication in 1202 of his Liber Abaci (Book of Calculation), and for the number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the Liber Abaci:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ...

This sequence is constructed by choosing the first two numbers (the "seeds" of the sequence) then assigning the rest by the rule that each number be the sum of the two preceding numbers. This simple rule generates a sequence of numbers having many surprising properties, of which we list but a few:

• Take any three adjacent numbers in the sequence, square the middle number, multiply the first and third numbers. The difference between these two results is always 1. • Take any four adjacent numbers in the sequence. Multiply the outside ones. Multiply the inside ones. The first product will be either one more or one less than the second. • The sum of any ten adjacent numbers equals 11 times the seventh one of the ten.

The Fibonacci sequence is but one example of many sequences with simple recursion relations.

Mathematics serves us well in finding order and patterns when observing nature’s models, systems, processes and elements for inspiration to drive innovation and be able to solve routine problems such as skin care.

Example…

Here’s a picture of a solar powered street lamp. Take a look at this photo, and then I want to ask you a question.

street lamp

Which of these two solar devices do you think makes most efficient use of sunlight?

In this picture there are two solar powered devices, not one. One is the street lamp. The other is the tree right behind it. Here’s the question:

Which of these two solar devices do you think makes most efficient use of sunlight?

The one made by humans, or the one made by nature?

Did you know this tree actually turns its leaves towards the light automatically? And that’s the least I can say. The tree is hyper-effective at harnessing scarce resources.

The reasons for this are many. Nature has such a treasure of tools she wants to lavish upon us, yet rarely do we stop and ask her really insightful questions.

When you look at the street sign, can you see any lessons borrowed from nature?

I sure don’t see many. The sign wastes tons of energy. The tree doesn’t.

Hint: 99% of skin care or acne treatment is like this road sign. It wastes 3/4ths of your money and time. Believe me my friend, you pay for EVERY BIT of that wasted money and time.

When you use energy the way the tree does – instead of the way the sign does – you get a lot more propulsion for the same amount of money.

In the middle of this sunflower are hundreds of seeds. You don’t have to look very hard to see layers of beautiful spiral patterns:

sunflower

Sunflower

Isn’t it beautiful? I think so. But the algorithm that placed these seeds serves a very practical purpose as well. It packs an optimum number of seeds into a very tiny space. And it uses Fibonacci numbers to do it. If you count you’ll see groups of 13, 21, 34 and 55 seeds, depending on which spiral you follow.

No other arrangement packs more seeds into a smaller space. It’s based on the Golden Ratio 1.618.

Golden Radio

Golden Ratio 1.618

The Fibonacci sequence obeys the recursion relation P(n) = P(n-1) + P(n-2). In such a sequence the first two values are arbitrarily chosen. They are called the "seeds" of the sequence. When 0 and 1 are chosen as seeds, or 1 and 1, or 1 and 2, the sequence is called the Fibonacci sequence. The sequence formed from the ratio of adjacent numbers of the Fibonacci sequence converges to a value of 1.6180339887...., called "phi", whose symbol is  or .

The ratio  = 1.6180339887... is called the "golden ratio" or "golden mean". A rectangle that has sides in this proportion is called the "golden rectangle", and it was known to the ancient Greeks. The golden rectangle is the basis for generating a curve known as the "golden spiral", a logarithmic spiral that is fairly well-matched to some spirals found in nature, and this fact is the source of much of the popular and mystical interest in this mathematical subject.

Seeds

45 degree Seeds

Man grows seeds at ‘normal’ 45 degree angles between each seed. See how much space is wasted.

Sunflower Model

Sunflower Model

Nature grows seeds using ‘irrational numbers.’ The angle between each seed is 1.618 radians, or 137.5 degrees. See how efficiently it uses space?

The Golden Ratio and Fibonacci numbers also appear in certain snail shells…

Snail

The Golden Ratio and Fibonacci numbers in snail shell

The snail must grow in such a way that its body remains more or less the same size in relation to its shell, otherwise the shell would become too heavy to drag around. Also the snail has to fit its body into the big end of the shell. Thus the most recent addition to the shell will maintain a more or less constant relationship with all the shell that has gone before.

The growth process is carried out in two stages: In the first stage the thin, transparent and organic outer layer is created, on which the calcified inner layers are deposited in the second stage. Specialized cells of the mantle secrete the shell material.

But this is not the most interesting about snails. What is surprising is that they have skin that is very similar to human skin, and they secrete their own skin care lotion, that protects, repairs, moisturizes and regenerates even their severely damaged skin tissues.

The lotion is created as a fundamental solution by their innate immune system, a machinery way more complex and sophisticated than any laboratory created by man.

A surprising complex skin care ingredient created by the innate immune system of a biological organism.

Scientists have characterized the secretion as a “serum” that supports immunity, avoids infection by microorganisms, and is made of macromolecules that act as nano-machines within the cells, moisturizing, scavenging and sequestering free radicals, and cleaning, repairing, and regenerating all the structures of healthy skin.

Macromolecules can be thought of as molecular machines, in the sense that they are modular, complex, have moving parts that carry out the same step many times over, and consume energy. They perform essential tasks in the cell, such as reading out and translating the genetic code; generating or converting metabolic energy; generating force to enable the cell to move; taking up, synthesizing or secreting enzymes, metabolites or other macromolecules; recognizing and reacting to signals from the outside world; to name but a few. Ultimately, the sum of all these assemblies defines the uniqueness of a given cell, an organism or an individual.

No biochemist in a lab can use a machinery as complex as that of the immune system of a living creature to create complete and balanced skin care ingredients of superior efficacy. Such machinery is capable of generating enormous chemical diversity through the processes of genetic recombination and somatic mutation, to create a biological solution totally compatible with living cells.

Testing the effects of the snail serum on human skin has provided us with insights about what is necessary for the effective care of human skin lesions and skin affected by infections and hard to heal skin disorders such as acne, acne scars, rosacea, … and many worrisome skin conditions.

We stumbled upon this discovery and we have engaged this naturally occurring serum to consistently get an edge, a natural efficiency that had remained invisible before our very eyes.

Now, this new skin care ingredient is here to stay and provide the world with an easy way to healthy, beautiful skin.