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Answer #1:

She would have 15 knots; adding up with the first rope's knots, the second rope's knots, the third rope's knots and the knots that's been created with every time a rope is combined with the other; 3+4+5+3= 15.

-http://mathworld.wolfram.com/Knot.html

-Praslov, V. V. and Sossinsky, A. B. Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology. Providence, -RI: Amer. Math. Soc., 1996.

-Przytycki, J. "A History of Knot Theory from Vandermonde to Jones." Proc. ----Mexican Nat. Congress Math., Nov. 1991.

-Reidemeister, K. Knotentheorie. Berlin: Springer-Verlag, 1932.

Short Biography of who's behind the knot theory

Kurt Werner Friedrick Reidemeister

Reidemeister's focus was on algebraic number theory and then later became interested in differential geometry. With this interest in geometry, Reidemeister wrote a sort of Principia Mathematica for knot theory, called Knoten und gruppen in 1926. The branch of geometry and topology that he created, knot theory, is based on group theory without the concept of a limit. His most significant contributions to knot theory are the Reidemeister moves, which are way of manipulating knots without changing their isotopic class.

Carl Friedrich Gauss

Knot Theory

Lord Kelvin (1824 - 1907)

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Introduction

The further elaboration and development of systematic arithmetic, like nearly everything else in which the mathematics of our [nineteenth] century has produced in the way of original scientific ideas, is knit to Gauss.

Archimedes, Newton and Gauss are all mathematicians of the same caliber, genius. Like Archimedes and Newton, Gauss contributed to the areas of pure and applied mathematics. He did pioneering work in the field of infinite series and is known for rediscovering Euler's law of quadratic reciprocity and wrote the first proof of that law. Gauss also came up with the algorithm for the Gaussian Blur, a popular algorithm in digital graphics. Gauss made his contribution to knot theory with analysis situs, which deals with the mathematical differences between simple and complex knots, which are easily discernible to the human eye but difficult to differentiate between mathematically.

Lord Kelvin was a scientific successor and had many interests in science. He released admirable publications, corrected lucrative (profitable) inventions, and worked with other amazing scientists of his time. Throughout his career, he has been beneficial to the broad field of science.

Kelvin's successes and contributions began at an early age. When he was ten years old , he had begun attending the University of Glasgow. Among many of his university awards there was a gold medal from 1839 for an essay "An Essay on the Figure of Earth," amongst many other university awards, which he would use for ideas until a few months before his death. His first contribution to science was in the form of papers published in defense of Fourier's work, when he was only sixteen and seventeen years of age.

In 1846, Kelvin was elected ‘professor of physics’ at the University of Glasgow, thanks to some requests on the part of his father, he would remain there until 1889. It was during this period that he published many of his papers (over 600!). Five years after becoming a professor, Kelvin was honored with membership to the very prestigious Royal Society.

Kelvin's inventions out-numbered many other scientists. His inventions included; the mirror galvanometer, an analog tide predictor, a compass resistant to the iron hulls of ships, and the absolute temperature, or ‘Kelvin scale’. Many of his inventions are still in use today, including the Kelvin scale, and the knot theory. One of Lord Kelvin's gifts to mathematics was inspiring others to inquire into the field of The Knot Theory.

Lord Kelvin received many honors before his death; including the knighting by Queen Victoria, him being the president of the Royal Society, being Baron Kelvin of Largs, and receiving the order of Merit. Lord Kelvin died on December 17, 1907, leaving the world with the spirit of his work.

The Knot Theory is a branch of topology that deals with links and knots. In topology, a doughnut is the same as a coffee cup, and a sphere is the same as a cube. It doesn't deal with the rigid properties of objects, such as angles and length, but instead, the properties that no amount of bending, twisting, stretching, or shrinking can change.

A knot is a closed, one dimensional (1D), and non-intersecting curve in three-dimensional space. From a more mathematical and set-theoretic standpoint, a knot is a homeomorphism that maps a circle into three-dimensional space and can't be reduced to the unknot by an ambient isotopy.

Throughout the history of Knot Theory, it's founders kept the theory alive by finding uses for the study. From the atomic theory proposed by Lord Kelvin, to the discovery of a DNA molecule in the form of a trefoil knot, a purpose and inspiration for knot theory always existed. The applications of knot theory today stretches through chemistry and molecular biology and into the world of quantum mechanics and the universal Theory of Everything!

Math Riddle Time (Created by Us)

Answer #2:

1, the only person that is assumed to be going to Vancouver is the narrator.

#1 A girl Scout member has three ropes. One of them has 3 knots, another has 4, and the last has 5. How many knots would she have in the first rope if she combined all of them in one rope?

There continues to be ongoing research in the field of The knot theory today. We feel that The knot theory will always be more than just a mathematical curiosity, and hope you enjoy our presentation!

Answer #3

They both weigh a ton.

Answer #4

Start one of the ropes on fire from both ends and the other one from one end. After a half an hour one rope will be completely burnt and the other will be half burnt. At this point you light the final rope from the unlit side and it will take 15 minutes for the remaining half of the rope to burn, for a total of 45 minutes.

Benefits of The Knot Theory today, in Math

#2 As I was going to Vancouver, BC,

I met a fisher-man with seven nets,

Each net had seven ropes,

Each rope had seven knots,

Each knot had seven ties:

Nets, ropes, knots, and ties,

How many were there going to Vancouver?

Class Activity

#3 Does a ton of ropes or a ton of knots weigh more?

Bibliography

#4 There are two ropes that both take exactly 1 hour to burn from end to end. You are unable to cut the rope. How can you burn the two ropes in a total of 45 minutes?

How knot figures can you do?

Knots appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone.

The pattern of the knot theory, is, itself, a useful proportion. Other knot proportions include the anatomy of the fundamental parallelogram, length of shortest geodesic, and volume. Modern knot and link summary efforts have applied these proportions successfully. Fast computers and intellectual concepts of obtaining these proportions make calculating these invariants, in practice, a simple task.

And yet Mathematicians, still, to this day, are trying to figure out the more secrets and discoveries of the Knot Theory.

Benefits of the Knot Theory today, in Science

The Knot Theory

Mr. Ghassan El- Kilani

Math 9

By Yasmine Jaradat & Noor Hmidan

17/01/2014

Thanks to Lord Kelvin because it was his belief that the universe was filled with an invisible and frictionless fluid called the ether. Atoms would be vortices in this fluid in the shape of knots. A table of knots, therefore, would be a table of elements. Thus, various scientists undertook the task of tabulating and theorizing over knots. When this concept of the ether and vortices died, knot theory diminished into a mere mathematical intrigue. Eventually, however, knot theory took on a new level of meaning when it appeared in the structure of DNA, and several theories for the underlying interactions between particles in quantum mechanics.

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