Continued Fractions I

An article introducing continued fractions with some simple puzzles for the reader.

LOGO Challenge - Circles as Bugs

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.

Using logo to investigate spirals

Gnomon Dimensions

Stage: 4 Challenge Level:

Here are the perimeters of $G_6$.

Here are the perimeters of $G_6$ rewritten in terms of their Fibonacci numbers ($F_1 = 1, F_2 = 1, F_3 = 2, F_4 =3$ and so on).

Could you draw diagrams showing in general how two gnomons fit together to make a third gnomon?