Concept
Fibonacci Circles
The Fibonacci Circles collection shows arrangements of circles whose diameter corresponds to the Fibonacci numbers. The diameter of a circle is therefore the sum of the diameters of the next two smaller circles. The colored areas grow as the square of the Fibonacci numbers.
Encircling Circles
In the Encircling Circles series, one circle is surrounded by the next larger circle so that they touch on the inside. The larger circle therefore encloses all the smaller Fibonacci circles. The only exceptions to this rule are the two innermost circles with a diameter of 1 cm, which touch each other on the outside as the origin of the image.
More pictures from the Encircling Circles series:
Encircling Circles II
The picture Encircling Circles I shows two series of Fibonacci circles alternating in black and white. Both series therefore contain identical circles.
The first series of circles spreads out like a wave front, starting in the center at the left edge of the picture with the red circle. Smaller circles are placed above the larger circles and cover them. Circles with odd Fibonacci numbers are painted black, those with even Fibonacci numbers are painted white, with one exception: the first circle with a diameter of 1 cm (the origin) is painted red. All the circles in this first series touch on the inside of the left edge.
The second series is a linear sequence of circles starting to the right of the red circle. Here, circles with odd Fibonacci numbers are painted white and those with even Fibonacci numbers are painted black.
Because the sum of the diameters of two consecutive Fibonacci circles equals the diameter of the next larger one, the circles of the second series always fit into the gap of the first series and are visible there due to their complementary color.
The outermost (black) circle has a diameter of 89 cm and encloses the two white circles. Encircling Circles II is therefore one Fibonacci unit larger than the related picture Encircling Circles I.
The picture illustrates with the second series of circles the well-known formula that the sum of the n first Fibonacci numbers is equal to the (n+2)th Fibonacci number minus 1: The sum of all circle diameters of the second series is the diameter of the large circle comprising the series minus the diameter of the small red circle.
The first series of circles spreads out like a wave front, starting in the center at the left edge of the picture with the red circle. Smaller circles are placed above the larger circles and cover them. Circles with odd Fibonacci numbers are painted black, those with even Fibonacci numbers are painted white, with one exception: the first circle with a diameter of 1 cm (the origin) is painted red. All the circles in this first series touch on the inside of the left edge.
The second series is a linear sequence of circles starting to the right of the red circle. Here, circles with odd Fibonacci numbers are painted white and those with even Fibonacci numbers are painted black.
Because the sum of the diameters of two consecutive Fibonacci circles equals the diameter of the next larger one, the circles of the second series always fit into the gap of the first series and are visible there due to their complementary color.
The outermost (black) circle has a diameter of 89 cm and encloses the two white circles. Encircling Circles II is therefore one Fibonacci unit larger than the related picture Encircling Circles I.
The picture illustrates with the second series of circles the well-known formula that the sum of the n first Fibonacci numbers is equal to the (n+2)th Fibonacci number minus 1: The sum of all circle diameters of the second series is the diameter of the large circle comprising the series minus the diameter of the small red circle.