Wednesday, August 22, 2007

Gauss y la suma de números

La historia es la siguiente: estaba Carl Friedrich Gauss allá por el año 1787 en la escuela. Tenía unos 10 años de edad. Con esa edad pasó lo que tenía que pasar, todos los niños empezaron a tirarse papeles, tizas, etc.

En ese momento apareció el profesor y cabreado como estaba, ordenó a todos los niños que, como castigo, le sumaran todos los números del 1 al 100.

El profesor debió pensar: ¡que idea más buena he tenido!. ¡Durante un buen rato, me dejarán todos estos mocosos en paz!.

A los pocos minutos, nuestro pequeño genio se levantó del pupitre, y entregó la respuesta correcta: 5050. El profesor, asombrado, debió pensar que había puesto un número al azar, y se dispuso él mismo a hacer la interminable suma. Al cabo de un buen rato, comprobó que, efectivamente, la suma pedida era 5050.

No es que Gauss fuera un calculador extraordinario, capaz de hacer sumas a la velocidad de un computador moderno. Gauss llegaría a ser uno de los mejores matemáticos de la historia, y los matemáticos no calculan: piensan

Lo que hizo Gauss fue lo siguiente:

Tenía que sumar los siguientes números:

1 + 2 + 3 + ... + 98 + 99 + 100

Pero nadie le obligaba a sumarlos por orden. Gauss se percató de un hecho singular: si agrupaba los número por parejas, tomando el primero y el último, el segundo y el penúltimo, etc., tenía lo siguiente:

(1+100)=101; (2+99)=101; (3+98)=101; (4+97)=101; etc.

Es decir, todos los pares de números sumaban 101. Como entre el uno y el 100 podía hacer 50 pares con esa propiedad, 50 x 101 = 5050.

Mas tarde, aplicaría este mismo principio para hallar la suma de la serie geométrica y muchas otras series.

Gauss y la campana

Friday, August 17, 2007

Educators of basic education: The present education

Escribi un articulo sobre mi vision de la educacion chilena en el año 2005, y hoy lo he encontrado traducido en otro blog.

Cosa rara que hayan hecho esto, eso quiere decir que algo tenia lo que escribi, y me anima a escribir nuevamente.

El post original se encuentra en Educalibre y la versión traducida esta en Educators of basic education: The present education

Se acaba WindowsUE

Según Imagen-A se acaba WindowsUE, quedando como último registro su versión 7.

Más información en el sitio oficial.

Debian cumple 14 años

Feliz Cumpleaños a Debian !!!!

Monday, August 13, 2007

Linus habla sobre GIT en Google.

Linus presenta GIT, su software de control de versiones. GIT es lo que actualmente se utiliza para el código fuente del Kernel de Linux.

Sunday, August 12, 2007

Marble Adding Machine

Wear Sunscreen

Wear sunscreen.

If I could offer you only one tip for the future, sunscreen would be it. The long-term benefits of sunscreen have been proved by scientists, whereas the rest of my advice has no basis more reliable than my own meandering experience. I will dispense this advice now.

Enjoy the power and beauty of your youth. Oh, never mind. You will not understand the power and beauty of your youth until they've faded. But trust me, in 20 years, you'll look back at photos of yourself and recall in a way you can't grasp now how much possibility lay before you and how fabulous you really looked. You are not as fat as you imagine.

Don't worry about the future. Or worry, but know that worrying is as effective as trying to solve an algebra equation by chewing bubble gum. The real troubles in your life are apt to be things that never crossed your worried mind, the kind that blindside you at 4 p.m. on some idle Tuesday.

Do one thing every day that scares you.


Don't be reckless with other people's hearts. Don't put up with people who are reckless with yours.


Don't waste your time on jealousy. Sometimes you're ahead, sometimes you're behind. The race is long and, in the end, it's only with yourself.

Remember compliments you receive. Forget the insults. If you succeed in doing this, tell me how.

Keep your old love letters. Throw away your old bank statements.


Don't feel guilty if you don't know what you want to do with your life. The most interesting people I know didn't know at 22 what they wanted to do with their lives. Some of the most interesting 40-year-olds I know still don't.

Get plenty of calcium. Be kind to your knees. You'll miss them when they're gone.

Maybe you'll marry, maybe you won't. Maybe you'll have children, maybe you won't. Maybe you'll divorce at 40, maybe you'll dance the funky chicken on your 75th wedding anniversary. Whatever you do, don't congratulate yourself too much, or berate yourself either. Your choices are half chance. So are everybody else's.

Enjoy your body. Use it every way you can. Don't be afraid of it or of what other people think of it. It's the greatest instrument you'll ever own.

Dance, even if you have nowhere to do it but your living room.

Read the directions, even if you don't follow them.

Do not read beauty magazines. They will only make you feel ugly.

Get to know your parents. You never know when they'll be gone for good. Be nice to your siblings. They're your best link to your past and the people most likely to stick with you in the future.

Understand that friends come and go, but with a precious few you should hold on. Work hard to bridge the gaps in geography and lifestyle, because the older you get, the more you need the people who knew you when you were young.

Live in New York City once, but leave before it makes you hard. Live in Northern California once, but leave before it makes you soft.


Accept certain inalienable truths: Prices will rise. Politicians will philander. You, too, will get old. And when you do, you'll fantasize that when you were young, prices were reasonable, politicians were noble and children respected their elders.

Respect your elders.

Don't expect anyone else to support you. Maybe you have a trust fund. Maybe you'll have a wealthy spouse. But you never know when either one might run out.

Don't mess too much with your hair or by the time you're 40 it will look 85.

Be careful whose advice you buy, but be patient with those who supply it. Advice is a form of nostalgia. Dispensing it is a way of fishing the past from the disposal, wiping it off, painting over the ugly parts and recycling it for more than it's worth.

But trust me on the sunscreen.