The Original™ Fibonacci Spiral Clock

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If you sum the squares of any series of Fibonacci numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number. This property results in the Fibonacci spiral, based on the following progression and properties of the Fibonacci series: Here’s what he did. It is possible to arrange squares whose side lengths are the numbers in the Fibonacci sequence into a rectangle. (This is the famous golden rectangle - here’s a previous post about that). Place the protractor on the point and mark the points on the circle with 30-degree increments. This will be helpful when marking the numbers in the step ahead.

Fibonacci spirals and Golden spirals appear in nature, but not every spiral in nature is related to Fibonacci numbers or Phi. Most spirals in nature are equiangular spirals, and Fibonacci and Golden spirals are special cases of the broader class of Equiangular spirals. An Equiangular spiral itself is a special type of spiral with unique mathematical properties in which the size of the spiral increases but its shape remains the same with each successive rotation of its curve. The curve of an equiangular spiral has a constant angle between a line from origin to any point on the curve and the tangent at that point, hence its name. In nature, equiangular spirals occur simply because the forces that create the spiral are in equilibrium, and are often seen in non-living examples such as spiral arms of galaxies and the spirals of hurricanes. Fibonacci spirals, Golden spirals and golden ratio-based spirals often appear in living organisms. Alternate spirals in plants occur in Fibonacci numbers. Before understanding the Fibonacci spiral we need to understand the Fibonacci number and Fibonacci sequence. Fix the minute and hour hand( Fibonacci spiral) as shown in the picture. This will be the base position that is both the hands are pointing towards 12. Mark this point by tracing the inner as well as the outer curve of the Fibonacci spiral on the metal sheet using a pencil/marker. A Fibonacci spiral gets wider or gets further away from the center for every quarter turn it makes. The spiral needle needs to be lightweight as well as stiff. This is the step that took a lot of time since I had to search for different materials. The solution that came to be was to use a 1mm plexiglass sheet but cutting the sheet into a spiral was a big hurdle. I came across an empty spraying can and experimented on it and was pretty much successful, so let's get started.

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Philippe Chrétien from Montreal, Canada, noticed that these numbers are all you need to express all the numbers from 1 to 12. The send one was an answer to a popular number riddle: If a pair of rabbits, male and female, can mate and every month their offspring produce a pair of male and female rabbits. How many rabbits will there be in one year? The Fibonacci spiral is a spiral that is built by constructing arcs that connect the points of these squares based on the Fibonacci sequence that is assembled in a spiral pattern. Once the glue is dry drill a hole on the center of the spiral of 5 mm( this corresponds to the hour shaft diameter as measured in the earlier step). Now start cutting the outer curve of the spiral using a tin cutter. Make sure your safety gloves are on, the metal burrs are razor sharp and can injure you. Take the help of an experienced person if you think you cannot handle it. Pinecones and pineapples illustrate similar spirals of successive Fibonacci numbers, with the example below showing the alternating pattern of 8 and 13 spirals in a pine cone.

Fibonacci popularized the Hindu–Arabic numeral system in the Western world primarily through his book Liber Abaci (Book of Calculation). The most common appearances of a Fibonacci numbers in nature are in plants, in the numbers of leaves, the arrangement of leaves around the stem and in the positioning of leaves, sections and seeds. Those patterns is extremely pleasing to the eye. We now have scientific evidence that our brains automatically recognize this pattern. Whether we have been genetically programmed to like it or we find it pleasing due to all the examples around us, the golden ratio has been used for a long time. The Fibonacci spiral gets closer and closer to a Golden Spiral as it increases in size because of the ratio of each number in the Fibonacci series to the one before it converges on Phi, 1.618, as the series progresses (e.g., 1, 1, 2, 3, 5, 8 and 13 produce ratios of 1, 2, 1.5, 1.67, 1.6 and 1.625, respectively) Now, measure 300 mm and mark a point on the centerline from the top edge(short edge ) of the sheet metal. Draw a perpendicular line from this point. Use this line as a base for bending the sheet.

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Anyway, just messing around with the concept. I could see how the software coding for adding a third tally would not present huge problems, but have no idea what complexity it introduces in the hardware.

The Fibonacci sequence is the sequence beginning 1, 1 and where each number is the sum of the previous two. Its first five digits are: Fibonacci numbers form a sequence such that each number is the sum of the two preceding ones, starting from 0 and 1. The second idea I had, which is still half-baked, revolved around playing with primary colors and secondary ones. If either a white or blue or green or red square were to move towards (or suddenly be) grey, purple, yellow, or orange -- then this could also serve as a signal about how many minutes, 0 thru 4, to add. I am using a standard 400ml spraying can and there is plenty of free space after wrapping the paper on the can. Once the spiral is cut it might have deformed depending on the skill to cut the sheet metal, don't worry flatten the spiral using a mallet.A Golden spiral is very similar to the Fibonacci spiral but is based on a series of identically proportioned golden rectangles, each having a golden ratio of 1.618 of the length of the long side to that of the short side of the rectangle: