During the mid-1990s, a spring toy that used kinetic energy was invented. The toy is called the Toroflux and has created a lot of buzz around the world. Jochen Valett, the inventor behind the toy, used a steel ribbon that he made into a torus sping. The beauty of the spring toy is that it has amazing energy minimizing abilities. Physics lovers, around the world, have been obsessed with the skills behind the toy. Students who studied physics are often found trying to use the toy to analyze the skills and perform tricks. One such student who was playing around found that the toy was able even to vanish. The curious student leaned toward mathematics to the dynamics behind the disappearing act of the toroflux toy. Burkard Polster who is a youtube pathologist is the one who instigated the study behind the vanishing capabilities of the Toroflux, decided to let the world in on the secret behind the concept.
The Toroflux Toy
The Toroflux toy is based on the reference of the Torus Knot, which is what mathematicians are familiar with. While there are infinitely different types of Torus knots, when they are applied in the right mathematical sequence they have the capabilities of vanishing and appearing randomly. The toy itself can rotate within itself and move down a shaft when it is threaded through. When you count the number of coils there are in a Toroflux; there are thirteen, However, if you close the Toroflux and then count the coils, you will find an extra coil making it fourteen instead of thirteen coils. It is indeed a mystery how the fourteenth coil appears and disappears. While it can stun math dummies, the concept behind the paradox is straightforward. The number of coils doesn’t add when they are joined together. Instead, when the length is slightly adjusted to increase uniformly throughout, one of the segments get removed. The increase in length is so small and extremely well distributed that it is barely visible.
The Mathologer’s World of Paradoxes
Burkard released a video to talk about the vanishing capabilities that others have been debunking about the Toroflux paradox as well as other paradoxes. Burkard has been contacted by other mathematics students who have been experimenting with the Toroflux concept, and one such person was Bill Russel from Bakersfield, California. Other paradoxes that have been sparked with appearing and disappearing acts are the ‘get the men off the earth’ paradox which magically, increases the number of men on a picture of Chinese men on a picture of the globe. Line paradoxes are another kind that has amazing appearing of extra lines and the disappearance of lines. The disappearing paradoxes don’t end with just lines and figures, but also has to do with the area of a square and a triangle. It is well known that when the area of a square that is made into a triangle is measured, the area remains the same. However, when you apply the Fibonacci sequence and look at the same, the area increases in the square.