RE: FLASH: The time has come... For flash 5 FLAs!

[.redstar.]

Branden,


Superb work, as always. One observation if I may, the 'snowflake fractal'

example is incorrectly attributed to Kotch. The correct name is Koch.


<off topic>

Niels Fabian Helge von Koch

Born: 25 Jan 1870 in Stockholm, Sweden

Died: 11 March 1924 in Danderyd, Stockholm, Sweden

Von Koch was a student of Mittag-Leffler at Stockholm University.

Von Koch's first results were on infinitely many linear equations in

infinitely many unknowns.

In 1891 he wrote the first of two papers on applications of infinite

determinants to solving systems of differential equations with analytic

coefficients. The methods he used were based on those published by Poincaré

about six years earlier.

The second of von Koch's papers was published in 1892, the year in which von

Koch was awarded a doctorate for his thesis which contained the results of

the two papers.

Von Koch was awarded a doctorate in mathematics by Stockholm University on

26 May 1892.

Between the years 1893 and 1905 von Koch had several appointments as an

assistant professor of mathematics. In 1905 Von Koch was appointed to the

chair of pure mathematics at the Royal Technological Institute in Stockholm.

In July 1911 von Koch succeeded Mittag-Leffler as professor of mathematics

at Stockholm University.

Von Koch is famous for the Koch curve which appears in his paper "Une

méthode géométrique élémentaire pour l'étude de certaines questions de la

théorie des courbes plane" published in 1906. This is constructed by

dividing a line into three equal parts and replacing the middle segment by

the other two sides of an equilateral triangle constructed on the middle

segment. Repeat on each of the (now 4) segments. Repeat indefinitely. It

gives a continuous curve which is of infinite length and nowhere

differentiable. If one starts with an equilateral triangle and applies the

construction, one gets the von Koch snowflake (sometimes called the von Koch

star) as the limit of the construction.

The von Koch snowflake is a continuous curve which does not have a tangent

at any point. Von Koch's 1906 paper mainly consists of a proof of this fact.

He also shows in the paper that there are two functions f and g which are

both nowhere differentiable such that the snowflake curve is

x = f(t), y = g(t) where -1 <= t <= 1.

The first person to give an example of an analytic construction of a

function which is continuous but nowhere differentiable was Weierstrass. At

the end of his paper, von Koch gives a geometric construction, based on the

von Koch curve, of such a function which he also expresses analytically.

Von Koch also wrote papers on number theory, in particular he wrote several

papers on the prime number theorem such as "Sur la distribution des nombres

premiers" in 1901 and "Contribution à la théorie des nombres premiers" in

1910.

</offtopic>


.redstar.




~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

NudeGuru.com is proud to sponsor the Flasher list

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        IT'S  THE  ART  OF  MONEY,  HONEY!

 Tips and Advice from some of the most popular Flash

 artists + industry power-brokers on how to hold onto

 your rights, negotiate contracts and get full value

 for your work.http://www.nudeguru.com from Franke James

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To unsubscribe or change your list settings go to

http://www.chinwag.com/flasher or email

helpchinwag [dot] com