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Spirograph Jr.

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In 1827, Greek-born English architect and engineer Peter Hubert Desvignes developed and advertised a "Speiragraph", a device to create elaborate spiral drawings. A man named J. Jopling soon claimed to have previously invented similar methods. [1] When working in Vienna between 1845 and 1848, Desvignes constructed a version of the machine that would help prevent banknote forgeries, [2] as any of the nearly endless variations of roulette patterns that it could produce were extremely difficult to reverse engineer. The mathematician Bruno Abakanowicz invented a new Spirograph device between 1881 and 1900. It was used for calculating an area delimited by curves. [3]

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While I can’t pinpoint exactly who invented the Spirograph, I found out about spiral drawing devices as the inspiration behind the toy. Popular in the late 18th century, these spiral devices used a rotating pencil to create spiralling patterns. Although they don’t look like a Spirograph and weren’t as popular, they were the first device to ever use a worm to create line patterns.

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The two extreme cases k = 0 {\displaystyle k=0} and k = 1 {\displaystyle k=1} result in degenerate trajectories of the Spirograph. In the first extreme case, when k = 0 {\displaystyle k=0} , we have a simple circle of radius R {\displaystyle R} , corresponding to the case where C i {\displaystyle C_{i}} has been shrunk into a point. (Division by k = 0 {\displaystyle k=0} in the formula is not a problem, since both sin {\displaystyle \sin } and cos {\displaystyle \cos } are bounded functions.) Originally developed as a drafting tool by a mechanical engineer named Denys Fisher, the distinctive wheels and rings of Spirograph cleverly combine the principle of art and mathematics in a way that has inspired and delighted generations. Create unique designs every time. or purse and store everything you need, though you’d need to replace the paper often. These are by far the most portable sets, but even large Spirograph sets are designed with portability in mind. They come with a carrying case in which to store wheels, pens, and paper so you can make art anywhere. Spirograph set features The 21st century saw the invention of digital Spirograph apps. These were the same as the classic Spirograph, but they were able to be replicated digitally. There are many different Spirograph apps available, and they’re also a lot less messy than the original Spirograph. The apps use a series of rotating discs to create spiralling patterns. So, while the digital Spirograph apps don’t look like the classic Spirograph, they are the same thing.

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Drawing toys based on gears have been around since at least 1908, when The Marvelous Wondergraph was advertised in the Sears catalog. [4] [5] An article describing how to make a Wondergraph drawing machine appeared in the Boys Mechanic publication in 1913. [6] If you’re not familiar, the apparatus involves a plastic cog, placed inside a circular hole with teeth, which has holes in it to place a pen/pencil through. Placing a pen in one of the holes and moving it around allows you to draw interesting patterns – the teeth of the circle and teeth on the cog will mesh to make the circle move and turn at the same time, and with the right pressure applied in the right direction, you can roll it around the inside of the circle, making interesting shapes. While many will have played with it and produced some interesting patterns, and presumably also had a vague sense that some maths is happening, I suspect many won’t have thought about it too hard. I certainly didn’t, until recently when someone gave me a mini-Spirograph kit as a gift. This inspired me to dig a little deeper into how this thing works, and what kind of shapes you can make with it. Looping the loop

Spirograph set size and portability

Round wheels: These basic wheels are probably the type with which you are familiar. They may have five to 35 holes. Each hole will create a slightly different pattern using the same wheel. Should it not be ‘R = 7/2 r’ in the 5th paragraph of the ‘How Many Points?’ section? Otherwise R < r

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