WisFaq!

Kettingbreuken

Hallo,
Wij werken nu met kettingbreuken. Maar zou u mij kunnen uitleggen wat nou eigenlijk het belang van kettingbreuken is. Waarom is het handiger als je sommige decimalen in kettingbreuken omzet?
Alvast bedankt

anoniem
24-2-2006

Antwoord

Het belang van kettingbreuken?

The Dutch mathematician and astronomer Christiaan Huygens (1629-1695) was the first to demonstrate a practical application of continued fractions.[6][5] He wrote a paper explaining how to use the convergents of a continued fraction to find the best rational approximations for gear ratios. These approximations enabled him to pick the gears with the correct number of teeth. His work was motivated impart by his desire to build a mechanical planetarium.

(...)

To give an example of their versatility, a recent paper by Rob Corless examined the connection between continued fractions and chaos theory. Continued fractions have also been utilized within computer algorithms for computing rational approximations to real numbers, as well as solving indeterminate equations.

Kijk dat zijn toch leuke dingen voor de mensen...

Zie de link bij Repeterende vergelijkingen.

WvR
2-3-2006