PHI, The Golden Ratio

After my previous post, you already know that I love everything related with numbers and especially those facts that combine numbers and real life.

So that, today I want to write a few lines about another very important number in our lives although maybe it is not recognized by as many people as it happens with Pi. I'm talking about PHI, also known as the "golden ratio". Another irrational number with a great presence into the Nature, but also used by sculptors, painters and architects since many centuries ago.

In fact, its name comes from the famous artist and architect Phidias who built the Parthenon in the Ancient Greece, a building where golden ratio is present almost everywhere.

We find the golden ratio when we divide a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

Many artists and architects believe that Golden Ratio makes the most pleasing and beautiful shape of a rectangle. There are even scientific studies which demonstrates that most of the people perceives this proportion as more beautiful than other ones.

By the way, one of the most famous series of numbers (Fibonacci series) is based in the golden ratio because each number of the series is the sum of the two numbers that precede it. This series floods Nature:

• Many flowers have a number of petals that belongs to Fibonacci series.
• Sunflower seeds follow spiraling patterns and each spiral is a number of this famous series.
• Something similar happens with pinecones and their seed pods.
  
  

  
    
  

  We can also find this amazing ratio at snail shells, nautilus, the cochlea of our inner ear and spiral galaxies. Even in destructive forms… just have a look at satellite pictures of a hurricane and you will see that harmonious spiral inscribed into imaginary golden ratio rectangles. But this is just a small piece of the cake, next post I will write about human body (face, fingers, the Vitrubian man…), animal bodies, reproduction, DNA molecules.
  

  
  
  
  Don’t you think it’s an amazing relationship between Maths and Nature?
  
  
  
  You can learn more about Phi on
  
  http://sciencepenguin.com/golden-ratio/

The Pi Day

As a Mathematics teacher I'm usually concerned about curiosities related with our life which are connected with this subject in one or another way. That most of the things which surround us have a Maths basis is a fact, but some of them have a special interest because they are weird.

The day before yesterday it was one of those special and weird days from a mathematical point of view. If we check the date at a newspaper caption maybe we won't notice it, but if we transform it into short format date, then we will realize that it was 3/14/15 which corresponds with the first 5 digits of Pi number. In fact we had an even more accurate "Pi moment of the day". It happened at 9:26:53 AM when the time figures added 5 additional decimal digits of this number.

The most special thing is that is the one and only Pi Day that will happen during current 21st century, so that it make it a little more special than other,  at least for all the people who knows the importance of this irrational number into our lives and our past.

For example, egyptologists have been fascinated by the fact that the Great Pyramid at Giza has dimensions related with Pi. The vertical height of the pyramid has the same relationship to the perimeter of its base. Just exactly the same as the radius of a circle has to its circumference.

There are also other really curious facts. One which always catch the attention of everyone is that the first 144 digits of this number add up to 666….the number of the Beast !!

Besides, Pi is related with many computing and communications situations, but they are quite difficult to explain with words. However, everybody involved with technical studies will confirm it.

So that, we can say that this has been a very special day.
 

You can learn more about Pi on

http://www.huffingtonpost.com/david-h-bailey/pi-day-314-14_b_4851011.html

The Best Teacher I've Ever Had

Education is a very important part of our lives, not only for what our future refers, but also because it forms us as a person. Furthermore, we dedicate a very important part of our infancy, adolescence and youth to it. Because of it we guard many recollections of this and of the persons who have taken part in our training, especially of those that more impressed us for any reason, or simply because we admire their way of being.

In my case, I will always remember my teacher Verónica, the best teacher of mathematics that I have had and better person. The first day that I knew her, it was so funny that she was called like me. Later, she was my teacher of this subject for 3 years. She not only helped me to understand this matter in its more difficult areas but in addition she was a great emotional support to me. To be honest she was very strict in class, but always she was worrying for each and every of her pupils, independently about our notes or about our behavior.

I am not the only one who remembers her as the best teacher of the world. When we met the class mates, the teacher Verónica always is one of the major topics of our recollections. In fact, a couple of years ago, after having lost contact with her because she changed her city of residence, we returned to talk with her because some of their students organized a surprise visit in order to see her another time. I will never forget her tears when she saw us appearing for the door of the high school in which she is employed nowadays. Since this day, we are in contact through e-mail and we can talk about our similar lives. She continues being the best teacher of the world!