Logarithmic spiral

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an image of a golden section in the shape of a circle with a rectangle

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

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the cover of an album with white circles on black background

The «spira mirabilis» (wonderful spiral) is a particular logarithmic spiral described for the first time by René Descartes and subsequently paid attention to by the Swiss mathematician and scientist Jakob Bernoulli, whose curve wraps around the pole without however ever reaching the starting point. Its peculiarity lies in the fact that the spiral has neither beginning nor end and, despite the infinite evolutions and rotations, always remains similar to itself. Bernoulli's adjective…

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a basketball court with an oval on the side and a half circle in the middle

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

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an origami flower is shown on a white background with blue paper in the center

Designed and folded June 2012. Folded from an octagon cut from a 30cm x 30cm sheet of Nicolas Terry's tissue foil. This is the top view of this model here. For the past few weeks I have been experimenting with various new fractal designs. Originally I was actually going to post a picture of this design, but while trying to reproduce it for the picture, I came up with a completely different idea altogether-- and this is the result! I am really satisfied with the result of this model. As the…

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a snail with a golden section in the middle

Does one always need to know what music is "about" before listening to it? It's head VS heart. Go with your heart this time and listen first. Connect your device to a decent sound system or enclosed headphones, and click the orange PLAY button: mm Alternatively, you could listen to the music at its URL: http://soundcloud.com/peter-gore-symes/fiibonaccis-rabbits-the-sound If you wish, you can read the score here. It will open in a new window so you can read it while listening: mm mm Many…

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an image of a spiral with numbers on the bottom and one in the top corner

You've seen logarithmic spirals, but here's the Spiral Logarithm! It has its radial distance to the origin equal to the (offset) logarithm of its arc-length: r = log(s+1). Pictured log base 2. I came up with this the other day, but didn't find it being constructed elsewhere.

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