Friday, January 20, 2012

The Golden Number

Dalí painted in 1949 a painting called Leda atómica. It represent centuries of mathematics and symbolic tradition (especially Pythagoras ‘ideas). It is a drawing based on the golden number, but it is making in a way that is not easy to see. Looking the sketch which Dalí painting on 1947, we can observe that Dalí care about the geometric aspect. Besides, the painting is based in the Pythagoras’ pentagon.

Lucía and Iratxe

Thursday, January 19, 2012

The Golden Number

In Montepellier, Spanish postmodern architect Ricardo Bofill, designed "The square of the number Golden". Ricardo Bofill, is one of most important Spanish architects and is highly regarded in the world of the architecture and urbanism. Place du Nombre d’Or or Plaza in Montellier, France was built in 1984. Its structure responds to the geometric principles of harmony, based on the rules of the number of gold. The perimeter of the square, of twelve metres thick, is occupied by houses. The floor of the square distributes the apartments in three semicircles, four corners and a gateway to the square. The semicircles consist of 12X12metres square modules distributed according to the geometry of the decagon. The curvature is close which causes an appearance of individual homes that stand out, whereas, there is a continuous internal façade. The houses of the corners and the door of the square are quite different.
Iratxe and Lucía
The Golden Number

Goya worked on this painting for the Spanish monarchy, in Madrid from the year 1780 until 1783. This picture represents the Royal family, the Kings Charles IV and Maria Luisa are the key figures.
In this painting the symmetry is not present, despite the fact that at first see it may seem. The axis of the composition is the child of red (dressed as this color to stand out that role) and is aligned with the painting that is on its back. The proportion that Goya used makes the right side, with respect to the axis, smaller than the left side. This is due to the Golden Number that is a synonym for harmony.
To give dynamism to the scene, because as you can see in the image everything seems to be straight lines, we can look at studied line that create the heads and the position of the feet of the people in the painting.

Iratxe and Lucía

Monday, January 16, 2012

SImilarity with the knob.

I think that the knob of the door i similar that the exercise weights.

Similarity with the whale

I think that modern submarines are usually whale-shaped.

Sunday, January 15, 2012


The CN Tower in Toronto, the tallest tower and freestanding structure in the world, has contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of Phi!



Renaissance artists of the 1500's in the time of Leonardo Da Vinci knew it as the Divine Proportion. In India, it was used in the construction of the Taj Mahal, which was completed in 1648.



Phi , the Golden Section, has been used by mankind for centuries in architecture
Its use started as early as with the Egyptians in the design of the pyramids. When the basic phi relationships are used to create a right triangle, it forms the dimensions of the great pyramids of Egypt, with the geometry shown below creating an angle of 51.83 degrees, the cosine of which is phi, or 0.618.


Fibonacci's Rabbits

The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances.
Fluffy bunnies
Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was...
How many pairs will there be in one year?
  1. At the end of the first month, they mate, but there is still one only 1 pair.
  2. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
  3. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
  4. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.
Fluffy bunnies family tree

The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
Can you see how the series is formed and how it continues? If not, look at the answer!
The first 300 Fibonacci numbers are here and some questions for you to answer.
Now can you see why this is the answer to our Rabbits problem? If not, here's why.
Another view of the Rabbit's Family Tree:
another view of same treeMultiples-of-Phi family tree
Both diagrams above represent the same information. Rabbits have been numbered to enable comparisons and to count them, as follows:
  • All the rabbits born in the same month are of the same generation and are on the same level in the tree.
  • The rabbits have been uniquely numbered so that in the same generation the new rabbits are numbered in the order of their parent's number. Thus 5, 6 and 7 are the children of 0, 1 and 2 respectively.
  • The rabbits labelled with a Fibonacci number are the children of the original rabbit (0) at the top of the tree.
  • There are a Fibonacci number of new rabbits in each generation, marked with a dot.
  • There are a Fibonacci number of rabbits in total from the top down to any single generation.

Alexandra Brancovean, Candela Megido, Aida Zapico


I think that a ladder plane is similar to a high heels.


I think that a toothbrush is similar to a comb.


I think that a boomerang is similar to the moon.


I think that a clock is similar to a dish