Interview to Mr.Professor Michio Kaku.

This is my own interview to one of the best researchers nowadays, the professor Michio Kaku, from the  University of New York.

I hope you enjoy it.

Solving a kinematic problem.

This is my video for the proof of how to solve a kinematic problem.
I hope you enjoy it.

The Unexpected Hanging Paradox.

The unexpected Hanging Paradox is a paradox about a person's expectations about the timing of a future event. This paradox is a situation of mathematic rules applied in wrong situations in real life; Let me explain you:

A judge condemns a prisoner on death row to be hanged next week by the warden, but before leaving, he makes sure the prisoner understands that it is going to be unexpected, so they will not tell him the exact date.

After thinking about how to escape from there, he remember what the warden said: You will be hanged in an unexpected date for you; therefore, the prisoner open his eyes and starts jumping, screaming and celebrating it: He knows he is not going to die.

After reading this, you might think either he is crazy or he has a way to escape, but non of them are right. Let's think about it: The prisoner knows he is going to die be in an unexpected date next week. Then, in case he is not hanged on thursday, then he cannot be hanged on friday, knowing that it would not be unexpected (only 1 day left of the week, obviously he will die on friday because there are no more days in the week, but it would not be unexpected, so it cannot be). Once we have eliminated Friday, same happens with thursday. If on wednesday he was not hanged, he will be on thursday, knowing that there are no more days left. The prisoners applies this hypothesis for the rest of the days of the week, and this makes him reach the conclusion that he will not die next week for sure. Notwithstanding, he is hanged on wednesday at 6 am.

Supposedly, even though the warden's statement to the prisoner was paradoxical, it ended up being true anyway. However, if the prisoner is no better at making inferences than he is in the problem, the warden's statement is true and not paradoxical; the prisoner was executed at noon within the week, and was surprised. This just shows that you can mess with the minds of people who can't make inferences properly. Nothing new there. But in case we follow logic and apply strictly the warden´s statement, and the fact that our prisoner in this case is is able to do all this reasoning, then his statement would be false and paradoxical.

Therefore, in conclusion, depending on the prisoner, I would or would not be able to "escape from the death".

This paradox give us another way of seeing math, in this case probability and way we have to predict future events: Mathematical-rules or statements applied in wrong situations give us results not possible in real life.

Photoelectric effect + Einstein's Biography.

Planck's hypothesis of 1900 about the main features of light was very badly received by the scientific community because it was breaking all the precepts of classical physics. It was not accepted until, in 1905, Einstein used it to explain an unexplained  phenomenon "the  photoelectric effect"  described by Hertz in 1887.

This mentioned "photoelectric effect" goes about electron emission of a metal when it's irradiated with electromagnetic radiation. However, not all electromagnetic radiations works, I mean, it has to be an specific type one, for example, it has to display a determinated frequency, and a minimum energy called " threshold frequency ". If the energy of the way does not reach this amount of energy, no electrons will be emitted.

The Albert Einstein's equation is the next one:

Where E=hxv ( energy of a quark), and E=hxv0 (where v0 it's the threshold frequency). So,
E0 + Ke(Kinetic Energy of the electron) = Ef( Final Energy).

Also this formula was so outstanding by the fact of new concept of quarks, as I mention before.
The concept of quarks was firstly introduced by Planck. But time later, Einstein tended to called fotons, those particles which forms the light itself.

Here I attach you a link in order to improve your knowledge about Einstein's history, one of the most important scientific in the world:

  http://www.youtube.com/watch?v=Xc6f_qF81BU

 

Polyhedron by Euler's formula.

I'm going to introduce you into a field full of beautiful mathematical formulas and probably one of the most useful due to its broad applications in chemistry, engineering, maths... As I said we are going to enter within one of the most beautiful mathematical formulas, Euler's formula. Space dedicated to issues of geometric objects that are more or less daily, the polyhedra, including the cube, triangular pyramid or tetrahedron, dodecahedron (whose faces are pentagons), the truncated icosahedron (the soccer ball), etc ... 

The study of polyhedra is of vital importance not only for the geometric study of them, for mathematical research, but also for its applications in diverse fields such as chemistry, mineralogy, biology, engineering, architecture, design or even art....

If  "C" represents all the faces of a simple polyhedron and "A" the polyhedron's number of edges/ridges and "V" represent the number of corners, then :

C+V-A = 2

The most outstanding fact is that doesn't matter how many cuts can displays a polyhedron, cause this cut is going to form another polyhedron and the relationship between them is going to be the same between its faces, corners, ridges/edges...( C+V-A=2).

Let's make an example of it.

We can see that this cube displays 6 faces (C=6), and also it displays 8 edges (V=8), and finally, we can see that the number of edges/ridges is equal to 12 (A=12).

So;

     C+V-A=2 -----------> 6+8-12 =14-12 = 2

And now, we can see here another a cut polyhedron, so as I mention the relationship has to be same as shown in the picture.

Prime numbers.

A prime number is an integer bigger than zero which can not be expressed as the division of two positive integer numbers with the exception of number 1 and itself.

Indeed, prime numbers can be defined as: "Numbers which can not be expressed as the product of two positive integer numbers smaller than the him."

Notice that number 1 is not included into the prime numbers. 

Let's make an example:

   a)Number 7 only can be divided by 1 and by 7(itself). And It only can be expressed as the multiplication of 7 x 1. In conclusion, as number  7 can no be expressed by either the division of two number different from 1 and itself we can say that 7 is a prime number.

    b) Number 15 can be divided by 1,3,5 and 15, because we can multiply 3x5, divide by 3, divide by 5 ...etc. In conclusion, as number 15 can be expressed by more than 2 number it is not an integer.

The prime term does not mean being relative of someone. It came from the Latin "primus", and it means "the first" (protos in Greek). The fundamental theorem of arithmetic states that every integer is expressed uniquely as a product of prime numbers. That is why they are considered "the first", because from the most primitive ones we are able to get all other integers. (Ex: The number 15 is obtained by multiplying the primes 3 and 5).

Finally, the firsts 25 primes numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 y 97, which all are smaller than 100.

   

The power of the integral

Regarding the power of the integral we can see differents aplications, for example calculate distances, areas, even volumes that surround us.

That's why our houses are part of simple shapes like squares. Even the columns/pillars are like a finite cylinder.

Now we are able to calculate it with a simple doble or maybe triple integral if necessary.
Also, in order to calculate the volume of some functions where "ROU" remains the same regarding the z axis, we also can create two planes( z=4. =0) in order to calculate the volume under the curve.

The possibility to be able to calculate the surface or area of a non flat shape is amazing to me. Because we can solve it trough a doble integral and with a simple procedure, thanks to the revisor coeficient.

Moreover, if you look further, even the lamp's shape can be inferred like a finit cone. That's wonderful.

In conclusion, when we talk about Calculus we are talking about a useful tool to explain our world.

Maths are all around us

Cristal screens at mobiles phones, cars, TV …Those ones are possible due to maths (talking in a deep way). Our cardiovascular system also is based on fluid equations. Searching at Google is possible because of algorithm, as well. Moreover, air roads follow a graph theory and our own computers work thanks to binary system which is based on mathematics itself. That’s amazing!! Isn’t it?

Indeed, some Spanish mathematicians like Diego Alonso stated that: “As long as scientific develop increases, more mathematics importance. They are the essential tool to improve other knowledge areas. They are part of investigation in several fields, as well. Nowadays, their presence has risen more than ever before, even though it’s pretty difficult to notice them because they are hidden by technology itself.

           -TALKING ABOUT MATHS IN OUR HOME:

Every day our maths dependence increases in an big quantity. This fact is a national problem because Spain’s education results were awful last year ( Spain was at the 48th place at Mathematics’ Olympiads).  As Miguel Angel Herrero says: “ Our mandatory task is not enough to live up to top countries like China, USA… etc”.

      -OUR EDUCATION SYSTEM IS NOT ENOUGHT.

Jose Letona states: "Spain’s education need a “better maths” instead of more quantity of maths hours. He also criticizes the memory method in several Spanish schools which is based on reading and memorizing all syllable instead of the learning method which work in a logical and deductive way".

He also shares with us that “ we live in a world where everybody tends to memorize everything, including formulas, equations… Where if you change any word at the problem statement, the student doesn’t know how to solve the problem. This reason is caused because they are not trained to think or evaluate the problems in a logical way”.

All of that may sounds very familiar, doesn’t it? Who hasn’t ever memorized an equation or a formula? This is a very normally situation which everybody has been through.

OUR SYSTEM                                                                         OUR NEEDED 
                                                                                                       SYSTEM

---------------->

  -MATHS HAVE TO BE UNDERSTOOD !!!

Manuel de León says : “ Childs often like maths at the beginning, but when they are 12-13 years old they usually lose their interest at them, because anyone can learn maths without making an effort, even though if you were very good at maths. It’s the same example than the musician one, I mean, if he doesn’t practice a lot, he'll probably not play music propertly.

Also, he added that: “ If you can not understand something, you will probably memorize it. Furthermore, this is the biggest mistake you can do, because if you memorize something, its learning will be very briefly. There for, the bad feeling which produces maths is due to the fact of failing several exams or maybe some argues at home”.

So, I hope you have learned something useful. Now you should know what is the correct way to enjoy, understand and pass maths subject. 

Sometimes making an effort in a accurate moment is not so sharp/difficult/boring because whatever you’ve understood will remain in your brain for a long time.

Jose Antonio Abellán Coll.

Introduction to the blog

This is my personal blog for mathematics divulgation. My aim it's to demonstrate you maths are more simple than you ever thought.

Maths, as the life itself are simple too. In fact, the most complex process in life are compounded of simple parts.The mathematician's method work by the same method, I mean, trying to simplify complex problems into several simple parts. Thus, I'll try to show you that maths have a lot in common with our daily day, in a practical, simple and clear way. I think the best way to learn it's enjoying what you're doing and this will be my aim: Trying to learn, but enjoying our task.

Maths it's all around us. One example could be when we're playing football, the ball moves by different mathematics equations( called, Kinematics ), that's amazing, wonderful !!. Isn't it?
     
Here  I let you this amazing experiment !!

PD: My team's project: "LaureateRoboGuide"