A couple of demonstrations of the sine and cosine of the addition of two angles

This is a problem that was send for us in MA1121, and although I haven't found my own way I've got two ways to demonstrate it that I found this early morning when I was studying for my quiz of today:

By similitude of triangles

Rotating the axes

Haciendo uso del hecho de que a cada punto del plano le corresponde un vector y de que los vectores se suman según la regla del paralelogramo, vamos a demostrar las fórmulas para el seno y el coseno de la suma de dos ángulos en función de los senos y cosenos de cada uno de ellos. Concretamente vamos a demostrar las siguientes igualdades: Rest of the explaination at http://gaussianos.com/el-seno-y-el-coseno-de-la-suma-de-angulos/

Perhaps you were doing this, and now you feel spoiled, if that's the case then I let you another problem from Gaussianos.com that is really fod for thought:

Demonstrate that every triangle ABC that verifies that

is right angled.

Life

It's been a long time since the last post and it is due to I have had to study a lot, but that has made me find several interesting things to post about, in this case about Math. There are many mathematics games and today I like to write about one of the most famous: The game of life.

John Horton Conway a British mathematician was interested in a 1940s ploblem presented by John von Neumann, a Hungarian-American mathematicist and computist who attempted to find a hypothetical machine that could build copies of itself, so he started to work on it and although that machine haven't been done yet, he could find a mathematical representation.

This mathematical model was very complicated and Conway focused on the simplification of the model, his attempt of simplification was successful and was named The Game of Life. The game was published by first time in the October 1970 issue of Scientific American, in Martin Gardner's "Mathematical Games" column and it consists of the following:

The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, alive or dead. Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

• Any live cell with fewer than two live neighbours dies, as if caused by under-population.
• Any live cell with two or three live neighbours lives on to the next generation.
• Any live cell with more than three live neighbours dies, as if by overcrowding.
• Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

The initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed—births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick (in other words, each generation is a pure function of the preceding one). The rules continue to be applied repeatedly to create further generations.

From http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life

Since its creation the game has been of interest for scientists from many fields including physics, biology, biochemstry, mathematic, economy and computer science because of the surprising ways in which the patterns can evolve.

In computer science it is as so freaking interesting that anything that can be computed algorithmically can be computed within Life, this of course has influenced the culture around computing at the point that the hacker embleme is a representation of a glider formation in the game.

The mutation and
movement of a "glider".

This particurlar formation has got the property of being a spaceship and they travel diagonally across the board, but this is not the only you can do with gliders. Among the things that you can build from gliders are counters, logic gates and one may also build a pattern that acts like a finite state machine connected to two counters. This has the same computational power as a universal Turing machine, so, using the glider, the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints: it is Turing complete.

 I think that after this intro you want to use it, so here are some Life programs that you can use in orther to know and discover more about this game. "Enjoy Life!"

• Conway's Game of Life, by Alan Hensel.
• Golly.
• Life32.
• Mirek's Cellebration.
• Xlife.

It has been given to us...

The second most powerful tool to past MA1211 (Fri Week 4)

Mehr um Deutsch zu lernen

Warnung: this post ist written in Denglisch, I do not like doing it like this either but I'm in level A1 ;)

Following my course learning Deutsch, I've found a couple more tools to work mit, ein für learn more Deutsch und another für practicing:

Aprendealeman.com. Its title is very explicit so I don't have to explain much about this site but I highlight that unlike other sites this offers the audios with pronunciation of the words and with an "understandablecaptable" speed. Apart from this the site also offers tongue-twisters -very useful for pronunciation- and things about Deutsch Kultur, for those who -like me- use the Sprahen to know more about the people who uses it.

Schubert-verlag.de. This site is in Deutsch, it offers exercises of all levels of Deutsch according to the programme levels (A1, A2, B1 ...).

This is alle for now und if you found any mistake in mein bisschen Deutsch bitte let me know it! :)

How to print at Biblio

Everyday we learn something! Printing stuff it's not big deal but I think it is good for we nuevos to have a guide with the detailed algorithm of printing things in the cheapest place in our college (today one of my friends prnted about 80 pages and it costs just 24 Bs :D).

Step 0. First of all obviously you have to have some credits in Biblio, if you haven't done it don't panic and read this post.

Step 1. Go to Biblio third floor and walk diagonally to the left and you will find a room with PCs.

Step 2. Use one of the indicated PCs shown in a list on a ticket office that is in the same place.

Step 3. Print the documents as you are used to, then a window will appear and in the box that says .... you gotta write your ID and finally accept -don't worry about the password. You can print as many documents as your credits listen.

Step 4. Go to one of the copiers that are in the same floor outside the room in the magazines section. Put your TAI on the scanner and the machine will start printing your sheets.

This is Sparta @ the USB

Background from mccrillisphotography, inspired by 300 :)

Einige Tools für die ID1311

Este martes de Semana 4 primer tengo parcial de ID1311, así que estube buscando herramientas en la web y he aquí algunas que me gustaría compartir con ustedes:

Deutsch mit Optimal A1. Blog de una estudiante de alemán en el cual explica claramente los contenidos más importantes del libro que estamos utilizando además de postear links relacionados y música en alemán.

Siguiendo con este mismo tópico altamente necesario para amenizar el estudio y afinar el oído les dejo el dos links a posts de Taringa con algo de música en alemán: Música alemana : mp3 + letras, Música alemana : Wir sind Helden ( 3 discos ) + letras. Además de estos grupos también pueden escuchar algo de los inicios de Tokio Hotel y si prefieres algo más serio pueden escuchar Rammstein y/o Lacrimosa.

Como complemento para el libro recomiendo la lectura de esta guía de alemán básico hecha también por un taringuero y chequeen otros posts sobre el tema en la comunidad Deutsch Lernen de Taringa.

Tschüs! :)

Semana de las Agrupaciones Estudiantiles at the USB

During this week the different student organizations that make life in our college will be presenting what they do at Auditorios. I visited the following:

ANIMEUSB

If you've seen from Dragon Ball, Bleach, Caballeros del Zodiaco and a long etcétera this is your group! They watch anime and sometimes they do vigils playing video games all night long :)

GUIA - Grupo Universitario de Investigaciones Astronómicas

They make a meeting each week and they discuss topics about austronomic like advances in the field and interesting events in the universe. When the can be seen from here they organize overnights in the campus in order to present such events -very useful to know where you can sleep when the bus left you after a Cervezada xD-.

USB SOLAR

This is a team that is building the second version of a sun-light-powered car that will compete in Australia

3D Arts USB

A new student organization that makes 3D graphics and animations, here is their first short film


CIRQUE USB

Also a new organization, although they weren't officially in the expo they were recruiting on Wednesday. For now they don't have a site but soon they'll get one because I'm in ;)

CITE - Centro de Investigaciones y Tecnología Electrónica

Its field is the development and applications of electronic, this stand was really funny because in the middle of the demonstration their toy car started to not to work well. They will be giving courses during this trimester +info cite30@gmail.com.

CEE

The best stand for me, they installed a stair at COM and when you were up they let you fall a few meters!

Week 2

I haven't could post since Monday for several reasons, I do apologize because of that but you know that time goes fast, anyway here a summary of what have happened during these days:

Tuesday

PS: don't get worked up because of the "Schleim", I love German language but let's face it sounds like that when we say an "ach", "och", "uch" or "auch" xB.

Wednesday

Shock in LLA111, all main ideas, support ideas and summaries wrong! remind this: not always the main idea comes from the content it might be given by the style. e.g.: Instrucciones para subir una escalera and Continuidad de los parques, both by Julio Cortázar.

 Thursday

My Maths notebook has just fell, and yes I'm gonna write about it; on Thursday 3-4 we only saw inequalities but there are a couple of thing that I'd highlight from this class: the first one is the concept of transcendental equation, concept that came up because of this equation from Calculus by Michael Spivack: x + 3^x < 4 and the other is another way of doing inequalities:

Friday

First quiz in my college life! 3,75/5 just two demonstrations and then prepa. Interesting things from the prepa:




Always try to understand why the fuck are things for.

4 women want to cross a bridge, it's night and they've got just one lantern. They can cross 2 a time the bridge and must always carry the lantern with them. They take to cross what takes the slowest. Which is the minimum time?
TIMES: M1=1 min, M2=2 min, M3=5 min, M4=10 min.

...and Cervezada at night :D