Week 4: Beauty

Laura

GOLDEN RATIO AND MUSIC

‎"Music is a secret exercise in arithmetic of the soul, unaware of its act of counting." --Gottfried Leibniz, philosopher and mathematician.

Is beauty subjective or objective? Is it on the eye of the beholder or is it an absolute truth? There are many ideas around those questions, and the conclusion seems to be the same always: It can work both ways.  An example for each one is shown below. First, subjective, subjectivity can be defined in many ways, however it can be simplified as “in the mind of a subject” so a typical example is that to get that many people agree about aesthetic judgments, is an impossible task; second, objective, objectivity also can be defined of many ways, but it will be defined as "inherent to the object" here. As an example “Caño Cristales” ubicated in Colombia will be used, as it is shown in the image below, its beauty is inherent to itself, it is called the river of 5 colors, and is one of the most beautiful natural places in the world. But... Is there any mathematical way to measure the beauty? And the answer is definitely YES. There is a universal ratio called, “The Golden Ratio”, as Tomas de Aquino said: “Senses are delighted in things with the due proportion”. Scientists agree than a beautiful body has the golden ratio present in many parts, such as Da Vinci showed in The Vitruvian Man. 

On the other hand, music has been an important way of enjoying since many centuries ago. Music is a point where art, science, mathematics, and letters are found; and as it should be guessed a beautiful melody must have the correct proportions, and this is the point where the Golden Ratio enters. But, what is the “Golden Ratio” or “Divine Proportion”?  The golden ratio is an irrational mathematical constant, approximately 1.6180339887; it is found many times in nature, architecture, films, music, etc., as an expression of beauty. Also there is a sequence called FIBONACCI that is shown below, and is closely related to the divine proportion.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 88, 144… 

Each number is the sum of the two before, and the relation between a number and the below is each time closer to the golden ratio.  So Fibonacci is a shown of beauty, an objective beauty measured with the golden ratio, or phi.

Many famous composers used Golden Ratio or Fibonacci sequence in their works, however it is not known if it was conscious or not, but there is a classical example: Bartók in his work “Music for Strings, Percussion and Celesta” where the rhythm of the xylophone solo opens the third movement based on the Fibonacci  Squence using the rhythm with sequence 1:2:3:5:8:5:3:2:1. He assigned a number to each note 

• DO   1
• RE    2
• MIb  3 
• FA    5
• LAb  8

And there are much more evidence: The fugue is done in 89 compasses, and there is a change in the compass 55. A strange representation of this theme is presented in the image below. 

Finally next video shows an amazing modern composition inspired on Fibonacci sequence.

More information:

http://www.educacion.es/exterior/ad/es/publicaciones/Aula_Abierta2_Musica.pdf

http://en.wikipedia.org/wiki/Music_for_Strings,_Percussion_and_Celesta

http://www.intmath.com/Numbers/mathOfBeauty.php

http://theblog.philosophytalk.org/2006/08/its_often_argue.html

http://theblog.philosophytalk.org/2005/03/beauty_and_subj.html

http://en.wikipedia.org/wiki/Fibonacci_number

Marisol

BEAUTY - SKIN

The skin is the part of the body that needs more care. Remember that a healthy skin means a nice one. Skin is a main part of a women’s beauty, that’s why we should take care of it in order to look pretty and young.

To eliminate blotches, patches, spots or blemishes apply a little bit of eye drops every 10 minutes during an hour.

If the blemishes are brown, lemon is the solution. You can apply lemon juice two or three times a day, BUT BE CAREFUL because if you expose the area to the sun, the blotches will get worse. Also you can apply lemon juice with a cotton ball just at night, and wash your face with cold water in the morning. Lemon is used as well to white freckles. A more elaborated trick to fight against patches in your face is to dice onion and left them into lemon juice for ten minutes, then take the remaining liquid and apply it on the spots leaving it for fifteen minutes.

¿do you want your face free of black spots? That is as easy as wash you face! To eliminate those horrible black spots just clean you face with a solution of warm water with an aspirin dissolved inside.

Exfoliate your body is easier than you think! Add a soup spoon of sugar into your cosmetic cream and rub it on your skin making little circles, doing so you will eliminate death skin. Salt has the same effect, but in that case the mixture is elaborated with thick salt, olive oil and rosemary.  This last mixture will clean and purify your skin, but it only can be used in your body, because the salt can damage your face.

Plants and fruits are also useful for caring your skin. Open a leave of aloe vera, put it on your skin and leave it. Doing so you will end up with irritations and sun burnt. In case you have dry skin take mangos peel and pass it backwards on your skin, if you rinse the peel before passing you will get a very smooth skin texture.

If you have stretch marks keep in mind that they are very difficult to eliminate, but here I will tell you two homemade creams that can reduced them. 1. Take the peel of five purple beetroot, peel of five peaches and a carrot core. Blend them altogether and apply them on white stretch marks. 2. Apply almond oil after having a shower or aloe vera gel before going to sleep. 

Remember to consume the amount of vitamins recommendable.

Carolina