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Mathematics

A few useful notions:

the angle between two vectors A and B is given by the formula
cos(theta) = <A, B> / (|A| * |B|);
where <A, B> is the scalar product of A and B. Neither A nor B may be null.
the scalar product of (a, b, c) and (x, y, z) is (ax, by, cz).
the projection of B on A is the following vector:
(<A, B> / <A, A>) * A.
A must not be null.
the vector product of (a, b, c) and (x, y, z) is (bz-cy, cx-az, ay-bx).
the logarithm in base b of x is ln(x) / ln(b), or log(x) / log(b), where ln is the natural logarithm and log is the base 10 logarithm.

Math Smarts: Nurture Not Nature
February 20, 2001

This article explains that mathematical abilities are innate in humans, and thus that anybody can learn them successfully.

Most people who find math problems difficult, Devlin said, haven't mastered the ability to trick their minds into thinking of math as TV, to fool their brains into making abstract objects seem real.

HAKMEM
January 12, 2001

Work reported in this 1972 document was conducted at the Artificial Intelligence Laboratory, a Massachusetts Institute of Technology research program supported in part by the Advanced Research Projects Agency of the Department of Defense. It contains some little known data which may be of interest to computer hackers. (Link updated on March 22nd, 2010.)

Astronomy

Cutting the space budget really restores my faith in humanity. It eliminates dreams, goals, and ideals and lets us get straight to the business of hate, debauchery, and self-annihilation.
-- Johnny Hart

Gomez's Hamburger
August 10, 2002

This page from the Astronomy Picture of the Day web site shows a photograph of a mouthwatering space hamburger, which is named Gomez's Hamburger. (This would make a great restaurant name, by the way.)

Changing the Earth's orbit
February 5, 2001

Some astronomers are proposing that we push the Earth away from the Sun some day, so as to compensate for the increasing heat that will be emitted by our star during the next billion years. The proposed technique would use the gravitation of a 100 kilometer asteroid. It would allow us to move other planets, like Mars, into a position more favorable to the development of life.

Astronomy Picture of the Day
December 20, 1998

This NASA site shows a different image or photograph of the universe each day.

Star Gazer
April 1, 1998

The world's first and only weekly TV series on naked-eye astronomy. This series can be seen on PBS throughout North America since 1976.

International Dark-Sky Association
March 8, 1998

An association that promotes the reduction of light pollution which prevents people in cities from seeing the stars at night. If you doubted that there was an association for Everything, you are now confounded. Amateur astronomy should be accessible to all, and it is a shame that inefficient lighting in many cities prevents people from admiring the spectacle of our Universe.

Skepticism

"To teach superstitions as truth is a most terrible thing."
-- Hypatia of Alexandria

Skeptic's Dictionary
November 12, 1998

This site gives the skeptical point of view about a great number of obscure subjects, like Edgar Cayce, facilitated communication, UFOs, etc.

The Quebec Skeptics Association
October 6, 1998

This is one of the largest skeptics clubs in the world and one that is very involved in educating the public. This club promotes rational and critical thought.

The Club is also offering 750'000$CAN to anyone who can scientifically demonstrate a paranormal phenomenon...

James Randi Educational Foundation
December 7, 1997

Magician James "The Amazing" Randi has created a foundation that offers more than 1,100,000$ to anyone who can demonstrate a paranormal phenomenon in a scientific test. Isn't it amazing that certain people are absolutely convinced that they have supernatural powers but that none of them seems interested in collecting such an amount of money? Food for thought...

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