Saturday, September 5, 2009

Calgary Eyebrow Threading Downtown

seem stupid, but ... Sumas

Leo experience in Silicon on a promotion from The Economist:

Subscribe to the digital edition: $ 65
Subscribe to the print edition: $ 125
Subscribe to the print and online : $ 125

What would you choose?

What if they only offer two of the options?

subscription to the digital edition: $ 65
Subscribe to the print and online: $ 125
Enlace
Think about it and then go to read In Silicon explanation of how to manipulate us these things.

Note: Since I have very clear if this entry is not math or public sinmultaneamente here and the blog of Professor Miguel .

Tuesday, August 11, 2009

Brown With Blonde Highlights Hair Extensions

endless and the search for beauty and recursion

The other day I suggested a way of showing that the sum of the first odd numbers is always a perfect square. Use chickpeas, remember?
In mathematics, sometimes the obvious is not always easy. When faced with a problem, often, the hardest part is selecting the right tool. Once this is chosen (well chosen, that is), the resolution becomes trivial.
Today I propose a problem to solve using a common tool but most of the fans do not know math: the ralación between algebra, geometry and arithmetic.
The approach is simple: How much is this infinite sum?
adding What is the infinite things that, as the mathematicians love. If you want to try on their own to stop reading and get back in time with the solution (1 / 3, in case you are curious and want to stop reading right now).

methods exist for adding this series easily, anyone who has made a first course in a Bachelor of Science known, but since this is a blog for men of letters I I save that way.

The first impulse is brute force: to make all these fractions in decimal numbers and put them into a calculator (better in Excel) to see what comes out. The sum of the top five is: 0.25

+0'0625 +0'015625 +0'00390625 +0,00390625 = 0.3330078125

if we add fractions, we see that the first decimal always 3, so if one is sufficiently clever, it can venture and hit the correct solution (1 / 3 = 0'333333 ...)

But in mathematics, as in justice intuition is not enough to solve. It must be demonstrated.
And brute force can be very effective, but is not elegant, and mathematics, as important as the rigor is the pursuit of beauty: Look at this picture

:
is a triangle. Let's put another triangle inside it:
the triangle we have divided into 4 equal parts (what he seems to have put a thong?). We are left with the central and painted blue. Blue triangle that represents a quarter of the large triangle.

We'll repeat the process in the upper triangle:
That blue triangle above represents a quarter of a quarter of the big triangle, that is 1 / 4 2
can repeat as many times as you want:
To sum just have to keep in mind that each tiángulo blue is the fourth of which is directly below. Therefore, the blue triangles chain represents the infinite sum we want to calculate.
Now watch the original triangle has been divided into three pieces exactly the same (I have painted different colors to distinguish them), and if the three pieces are identical, then each of them represents 1 / 3 of the triangle.

Therefore our infinite sum of fractions (or triangles) is 1 / 3.
You see, math is not enough that all things are correct, it is also important that they are beautiful. I know that for one who had bad experiences in mathematics at school, talking about beauty in a problem is almost a provocation, but I do not deny that, at least, is smart. It seems to me wonderful.

Wednesday, August 5, 2009

How To Roll A Dutch Master Palma

Google

This story today they appeared as national news a few days ago.
Let's do an experiment. Open another browser window Google page and type Varcelona well, with V of Warsaw. get a lot of search results , but what we are is what comes up: If Google detects that the search word is misspelled we stand corrected.
Did you mean: Barcelona.
And if we click on the suggestion, it disappears.

Now repeat the same with the word Recursion. Google is proposing to do the search for the term recursion, but when we click on the suggestion, the same suggestion back out, over and over again, ad infinitum.

This is a programmer's joke from Google that shows the fine sense of humor they spend. Let's try to understand the joke.

In mathematics called recursion recursion or (two palabros que no existen en español, por cierto. El término correcto es recurrencia ) a una manera de escribir sucesiones de números en la que cada término se calcula a partir de los anteriores.
Por ejemplo, la famosísima sucesión de Fibonacci:
1, 1, 2, 3, 5, 8, 13, 21, ...
en la que los dos primeros números son 1 y 1 y a partir de ahí cada uno de los elementos se calcula sumando los dos que tiene detrás.
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13

La manera de escribir esto usando la recursión es:

F 0 =1
F 1 = 1
2 F = 0 F + F 1 = 1 +1 = 2
F 3 = 1 F + F 2 = 1 +2 = 3
... F
n = F n-2 + F n-1


words, to define an element refers to the definition of the element in smaller cases, and until the case but simple, which is defined numerically.
For example, we calculate F 5 , 5 th term of the sequence Fibonacci:

F 5 = F 3 + F 4

therefore, must first calculate the 3 rd and 4 th (ie F 3 and F 4 )

F 4 = F 2 + F 3
F 3 = F 1 + F 2


Whereupon the 5 th term would be (the parentheses are only to separate and not tiing):

5 F = (F 3) + (F 4 ) =
= (F + F 1 2) + (F 2 + [F 3]) =
= (F + F 1 2) + (F 2 + [F + F 1 2])

But F 1 = 1 and F 2 = 1, so that to calculate F 5 just replace the previous formula: F
5 = (F + F 1 2) + (F 2 + [F + F 1 2])
5 F = (1 +1) + (1 + [1 +1]) = 5

other words, to calculate a number use your own definition as many times as do need to get to the simplest case. You try to calculate other terms for themselves, help them understand.

The Google search does the same thing: If you are asked to find recursion recursion is proposing that we seek, and if we accept the suggestion we again make the same suggestion, and so on to infinity.
For Google, recursion is an endless recursion.

Note: This form of calculation is used by computers to perform complex tasks, split the task into smaller ones recursively up to a simple case easily solved. Two examples:
1. Management de un conjunto de números:
Para ordenar una lista de números se divide la lista en dos trozos, se ordenan cada uno por separado y luego se mezclan. Para ordenar cada uno de los trozos se utiliza el mismo procedimiento recursivo.
2. Buscar un número (o una palabra) en una lista no ordenada:
Se divide la lista en dos partes y se busca en una de ellas. Sino está se busca en la otra mitad. Cada una de las búsquedas se hace usando el mismo procedimiento. Aunque parezca mentira los ordenadores encuentran las cosas antes usando este método que mirando uno a uno los elementos de la lista.

Saturday, August 1, 2009

How To Predict Baby's Eye Color

perfect squares and odd numbers (post 3 chapters)

CHAPTER 1. The anecdote.
Jorge tells me a curiosity about the square roots of some numbers and their relationship with the odd numbers:
1 +3 = 4. Its square root is 2 (we added two odd numbers)
1 +3 +5 = 9. Its square root is 3 (we scored the first three odd)
1 +3 +5 +7 = 16. Its square root is 4 (we scored the first four odd numbers)
1 +3 +5 +7 +9 +11 +13 +15 = 64. Its square root is 8 (we scored the first eight odd)
etc.

CHAPTER 2. The theoretical rollazo .
This property of numbers is known from Tartaglia times (s. XVI) and even before:
The sum of the first n odd numbers is always n 2.
or also:
1 +3 +5 +...+( 2n-1) = n 2
Therefore, it is logical that if we add 8 consecutive odd numbers, square root result is 8.

Note: (2n-1)
is how to represent an odd number either: if we take a number n is multiplied by 2 we get a number, and if you subtract 1 what remains sure is
odd

CHAPTER 3. Demonstration practice.
This has a very simple demonstration using the known method of chickpeas: Take a humble
Thumb:

1 = 1 2
We will form a square by adding chickpeas:
1 +3 = 4 = 2 2
Note that we have added 3 chickpeas, and so we now have four chickpeas. 4 is a perfect square (2 2).
Note: The perfect squares are the numbers that can be put into a square using chickpeas. Let
. Now I will put more beans to form a square:

1 +3 +5 = 9 = 32
5
I added chickpeas. Now my square has 9 peas (3 2 )
Next step: Build a square a little larger.

1 +3 +5 +7 = 16 = 42
I added 7 chickpeas. Now my square is 16 beans (4 2 ).
Let's do it again. A square slightly larger:
1 +3 +5 +7 +9 = 25 = 5 2

can continue this procedure until you achieve the necessary number of chickpeas to make a stew, although from here strongly recommend to leave it after a suitable date.
And this is demonstrated and explained the fact that adding odd numbers, the result is always a perfect square.

Note: If beans are not available, you can use lentils or other legumes, but I assure you somo best understand this is to use slices of chorizo. In this case it is recommended practice until it is understood and beyond.

Friday, July 31, 2009

Sims 3finding The 3rd Relic

phrases with a certain mathematical sense (2)

A proposal to add another joke Raquel logical
L Leon begins and ends with T.

If not caught read it again.

Wednesday, July 29, 2009

How Do You Get Rid Of Tophi

Hiels Henrik Abel. A genius with no luck

Niels Henrik Abel (1802-1829) was a Norwegian mathematician (although born and died Danish Swedish) was born, he developed his career and died in the early nineteenth century. It is a contemporary of Byron, Espronceda, Beethoven and E. Galois, another French mathematician whose life keeps certain similarities: Both died young, they worked in solving equations of degree greater than 5, and both represent the romantic intellectual model that was both in his time.

Abel's name is related to many algebraic structures, some theorems on equations and in many astronomical concepts (one of the largest craters on the moon named after him) and paid tribute mathematicians giving its name in 2002 to celebrate bicentennial of his birth, the equivalent of Nobel Prize in Mathematics (Did you know that does not exist, nor will there ever a Nobel Prize in Mathematics? one day I'll talk about that.)

Perhaps those who suffered from this madness called small Modern Mathematics remember the name of abelian groups. Yes? Abel it is that which we speak.

Abel's life was marked by bad luck. I happened to be born in what today would call a dysfunctional family, with his father and alcoholic mother. His father, who was a pastor and political enthusiast who championed the cause of the independence of Norway, died when young Abel only had 13 years until he was 19, his family endured much hardship, but would be more accurate to say that went hungry. Fortunately, Abel was able to continue their studies and the age of 19 won a scholarship that allowed him to enroll at the University of Oslo.

in Oslo noted for his ability in algebra and in particular in resolving equation fifth grade. He once thought he had found the formula to solve the equations of fifth grade, but by analyzing their solutions concluded that this was impossible, and in parallel with Galois, who never met showed the impossibility of its resolution. He published his findings in 1824 in language so vague that it was not able to make him understand any of his environment. Obscure language that became the mark of the house and possibly because their work was not recognized until more than 20 years after his death. In the century

XIX being Norwegian was not exactly an advantage, so if the young Abel wanted to hobnob with the elite mathematics had to go to Germany or Paris, so he took his most important (on a thing called elliptic functions) and the minimal scholarship Swedish government embarked on the conquest of Germany. Before departure, and by way of letter sent to Gauss a treatise on elliptic functions, that never read (probably lost it or never even received.) In Berlin, while awaiting the response of Gauss, Abel met Crelle, engineer (he built the first railway track in Germany) and a lover of mathematics mathematical journal founded the most important of the day: The Journal de Crelle.

Crelle The friendship lasted a lifetime Abel, and beyond his death, addressed Crelle Abel received the recognition they deserved and that life was denied. For six months steadily Abel published in the Journal, but that did not give to live. The scholarship was running out and his health began to suffer from the difficulties suffered in Berlin (he lived for several weeks on the street).

disappointed by the silence of Gauss decides to go to Paris, where he worked the "other" big mathematics: Legendre, Fourier, and Cauchy. Abel sent a report of its work to the Paris Academy of Sciences seeking a professorship, or scholarship or something to let him continue his work. Fourier, secretary of the Academy of Sciences in Paris, commissioned Legendre evaluation. Legendre received the report and, without reading it, lost it. In their defense I must say that I had more than 70 years and was no longer the work of discovering young talents. In fact he died six years later. Abel
When asked about the matter, Fourier resend asked him again, and this time he charged that evaluate Cauchy. Cauchy was a great mathematician, but it was a good person, you may discover the genius that Cauchy had ahead and decide to hide the papers or postpone the decision indefinitely Abel because it aimed to "throne" of Fourier (Chair Academy of Sciences) and a guy like you probably Abel had departed from the race or at least would have overshadowed. To get an idea of \u200b\u200bwho we are talking about: Cauchy was denounced by one of his students to appropriate the results and publish them with your name. The fact is that the papers in the hands of Cauchy disappeared again.
Meanwhile, Abel and can survive in Paris, thanks to the supports that young mathematicians as Crelle, Poisson and especially Jacobi. But even the most strong wills are broken and in 1826, less than a year after have come to Paris, Abel, seriously ill with tuberculosis (was romantic even for diseases) decides to return to Norway. There, deep in debt to accept any job that comes to pass, from school teacher to mushing.

However, Crelle, his best friend kept going to get a job that let him live in mathematics, and eventually got him a professorship at the University of Berlin, since that would have guaranteed a good economic position the rest of his days.
Unfortunately it was too late: Abel died almost destitute, sick tubrculosis in April 1829. Two days after of his funeral, at his home received the appointment letter from the University of Berlin.
A sad life, chaired by bad luck, the man who could have been the greatest mathematician of the nineteenth century, and worth Heredea of \u200b\u200bGauss.

Fissure Mount And Blade

REOPENING CLOSED FOR VACATION TIME

Ahem, ahem.
Hello?
Is there anybody there?
me, I'm home.
After a few days mulling over the issue, weighing the pros and cons, my chances of writing, the time you'll have next year's ... I decided to reopen the site.
discipline as I've updated at least once every ten days. Let's see if I can.
For now I leave you with an entry that I published the other day in The Blog of Professor Miguel on Niels Henrik Abel.
And we'll try to put a new design and a new header.

Saturday, June 27, 2009

Køb El Santo Maske






... CONTINUE ...

Tuesday, June 9, 2009

Is There Bluetooth In Psp

We Dance? - Fiesta on June 12 - The Olga Vazquez - invite the attack Sienvolando and Art Mural Villa Arguello

-----------¡ Fiesta !------- JUNE 12 -----

You Dance?
"we must harden without losing the tenderness

** ** Catalunya
Madness ** ** Mansa
** Flamingo ** Smoking
** pants ** Pollera

Artistic interventions
:

Collective ** ** always **
Clowns: Panzucho and Feliche ** **
high level Presenters: Di Tomasso and Fantagucci Tero
** ** Dj. **
fight

+ Video projection early
+ ambience


Invite: Sienvolando and Art at

Attack Friday, June 12 22hs. CS

VAZQUEZ OLGA 60 and 10 and 11 - La Plata


Fiesta
-----------¡ JUNE 12 !-----------

Online Gay Cruising Toronto



Muralists Brothers Tello, Sienvolando group and the local people painted the front of the club. A colorful club, a club in the neighborhood. Sunday May 17, 2009. 126 esq 62, La Plata