Funny things: The Elevator.

Here I have one of the funny photos I have told you in the presentation of the blog.

In this picture, we can see two papers; the first one says (El ascensor sube solo al segundo piso sin pasar por el primero) "the elevator goes only to the second floor without going through the first floor".

And in the second paper we can see (Eso es imposible, firmado Bolzano) "that is impossible, sign Bolzano".

The number 1089

If you write a number with 3 digits without being palindrome, and if then you change the order of the digits (ABC → CBA). Now we have the number ABC and CBA, so we make a subtract of the smallest to the biggest one, having a result (DEF).  And now if we make the same thing changing the order we will get FED, and if then we make a sum of DEF and FED you will get always the same result.

1089

This could sound strange and also impossible, but it’s mathematics. Try it. You will always get 1089.

Now I will explain you why is this possible.

When we take the first number (ABC) we are taking 100A + 10B + C.

(A is the cents, B is the tens and C is the units)

Then we have to change the order, ABC → CBA, and then we have 2 numbers, so we have to make a subtraction of the smallest to the biggest one, subtracting these two numbers we get 100 (AC) +10 (BB) + CA = 100 (AC) + CA. Having assumed that A> C, obviously must be C <A,0 we have to add and subtract 100 units so the result won’t change: 100(A-C-1) +90+(10+C-A).

We can verify that this number always has the 9 in the tens position and also the sum of the first and the third number (AC-1 +10 + C + A) is also 9.

And also if we now change between them the first row and the third one and we make an addition we have this result:

100(A-C-1)+90+(10+C-A)+100(10+C-A)+90+(A-C-1)= 100A-100C-100+90+10+C-A+1000+100C-100A+90+A-C-1=1089

The number 153

The number 153 has very peculiar properties :

It is the smallest number that can be expressed as the sum of the cubes of its digits :

153 = 13 + 53 + 33

It is equal to the sum of the factorials of the numbers from 1 to 5 :

153 = 1! + 2! + 3 ! + 4! +5 !

The sum of its digits is a perfect square :

1 + 5 + 3 = 9 = 32

The sum of its divisors (excluding the number itself ) is also a perfect square :

1 + 3 + 9 + 17 + 51 = 81 = 92

Moreover, as can be seen , is the square of the sum of the digits.

Can be expressed as the sum of all integers from 1 to 17 :

153 = 1 + 2 + 3 + 4 + ... + 15 + 16 + 17

This means that 153 is the seventeenth triangular number .

Is divisible by the sum of its digits :

153 / (1 + 5 + 3) = 17

Can be expressed as the product of two numbers formed by the digits :

153 = 3 · 51

It can also be expressed in this curious way :

135 = 11 + 32 + 53

The sums of powers 0, 1 and 2 of its digits is equal to the product of them :

10 + 51 + 32 = 1 · 5 · 3

                      MY LIFE AND MATHEMATICS

My life and mathematics have always gone together. Since I was young, I have had the facility to solve math easily. It is obvious that when we are young it is not the same as when we grow up. When we are young the king of the classroom was the one who was able to solve a sum of more than two digits, such as 43 + 67. I was "advanced" because my father was concerned with teaching an advanced course always higher than mine, he always told me, “You’ll thank me in the future" and I finally understood when I got to 1st of “bachillerato” that he was right, the doubts of the integrals and other advance operations were already answered. To have an advance level in maths against my others classmates was not a hard thing for me. That facility makes me love the subject and also other subjects related to maths like physics or chemistry.

This made my life, short for now, were directed to consider a career in science technology (like my father). Although my dream was to be a fighter pilot , at the end I opted to study a related engineering engines , machines and try to get to devote myself to what my father was engaged ; engineering.

Installing and removing things has always been one of my passions from small toys that I bought to remove and fix the engines that fell into my hands.

Another of my obsessions shared with my family to study abroad as much as possible of the race and that made me opt for EMU and finally here I am ... Studying a career directly related to mathematics and a future projection attached to study and work abroad.

Since it is the first post not sure what subject to do, so I liked the idea that will lift base have to look at other blogs as I get to study something as related to mathematics and joined from very small to my life thanks to my father.

In return I have to say that in every post put a phrase or image gracious, most of not all in Spanish but explain them in English, but with the funny miss translation.

                          PRESENTATION OF THE BLOG

The blog is going to be written for the spreading of mathematics and others sciences likeness to maths.

This blog is being writing by a first year engineer, that studies at the UEM ( Universidad Europea de Madrid ). And the purpose is to contribute with the mathematics divulgation by uploading several posts which some of them will include special contents like videos, photos and also an interview.