Who was Theodorus of Cyrene? Theodorus of Cyrene was a Greek mathematician who lived in the 5th century B.C. He was a student of Protagoras, a follower of Pythagoras, and a teacher of Plato and Theaetetus. He is best known for his contribution to the theory of irrational numbers.
2. What is an irrational number?
An irrational number is a number that is random, but can have somewhat of a patterns. Irrational numbers also never stop, don’t repeat or terminate, and can’t be made into fractions. An example of an irrational number is pi (휋.)
3. How does the Wheel of Theodorus help you draw an irrational number? The Wheel of Theodorus is a spiral that illustrates irrational numbers. The wheel is started by first drawing a right triangle with equal legs, and a hypotenuse
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Why do you think that finding this pattern was important to Theodorus? Why is it important to us in the present day?
I think that discovering this pattern was important to Theodorus because it proved that the square roots of numbers from 2-17, excluding perfect squares, are irrational. It also shows that we can describe relationships and predict patterns for irrational numbers.
6. Do you think your wheel accurately represents irrational numbers?
I think that my wheel somewhat accurately represents rational numbers. I did my best to follow the pattern of the spiral and draw perfect right angles and even lengths. However, I believe that no one could draw an absolutely perfect Wheel of Theodorus.
7. Do you think that there is a more accurate way to draw irrational numbers in the present day?
I think that you could possibly draw irrational numbers more accurately on a number line. As I previously stated, the Wheel of Theodorus can never be truly perfect due to human error, so a number line could perhaps be more accurate.
8. What can we learn from the Wheel of Theodorus?
We can learn that the square roots of numbers from 2-17 are irrational, excluding the perfect squares of 4, 9, and
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
"What shall I say of the steadiness and exactitude of his hand? You might swear that rule, square, or compasses had been employed to draw lines which he, in face, drew with the brush, or very often with pencil or pen… this ...
Evariste Galois was a French boy born in Bourg-La-Reine October 25th 1811 to May 31st 1832. Born with both parents well educated in classical literature, religion and philosophy.There was never a record of mathematics in is family. Evaristes father was a republican who was head of the Bourg-la-Reine’s liberal party. When he was 10 his parents send him to a college in Reims where he got s grant. Soon his mother changed her mind thinking he would b defenseless on his own so she kept him home. His mother taught him his education until the age of 12. As a child he was never recorded to show any interest in the studies of mathematics. When he turned 14 he enrolled in his first school lycee of Louis-le-Grand in Paris where he took his first math class and he began his path to his future goals.
During the course of this almost comic sequence of events, a major chapter in the history of mathematics was closed. The story highlights the way math has developed over time and requires effort to sort through the various cases before a nice formulaic approach can be determined and shared with the world. Math students should be encouraged by reading the lives and work of the scholars before them who persisted at finding the underlying structure of our number systems.
Leonardo wrote numerous books regarding mathematics. The books include his own contributions, which have become very significant, along with ancient mathematical skills that needed to be rev...
There are six diagonal lines. At one end there are circles on them giving the impression of three circular prongs. At the other end the same size lines have cross connecting lines consistent with two square prongs. These perceptions can violate our expectations for what is possible often to a delightful effect.
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe.
The debate regarding Pythagoras and his theorem is very strong because not much is known of him since neither he nor his pupils left many writings, thus we only know some facts from contradicting accounts written two centuries after his death. However, it is now known that he did not discover the Pythagorean Theorem nor the connection established between musical intervals and simple
The recursive sequence of numbers that bear his name is a discovery for which Fibonacci is popularly known. While it brought him little recognition during the course of his life, is was nearly 100 years later when the majority of the mathematicians recognized and appreciated his invention. This fascinating and unique study of recursive numbers possess all sorts of intriguing properties that can be discovered by applying different mathematical procedures to a set of numbers in a given sequence. The recursive / Fibonacci numbers are present in everyday life and they are manifested in the everyday life in which we live. The formed patterns perplex and astonish the minds in real world perspectives. The recursive sequences are beautiful to study and much of their beauty falls in nature. They highlight the mathematical complexity and the incredible order of the world that we live in and this gives a clear view of the algorithm that God used to create some of these organisms and plants. Such patterns seem not have been evolved by accident but rather, they seem to have evolved by the work of God who created both heaven and
In conclusion it really is fascinating how a simple sequence can have unexplainable links to complex math and nature. Why would a bee’s family, sunflower seed, a master’s painting and the golden ratio all be linked by one sequence? I really enjoyed studying this topic because it remind us that math is not only about binomial expansion but also about the beauty of our world. This prove how complex are world is and really shows the beauty of our galaxy, because yes our galaxy follows the golden ration.
Carl Friedrich Gauss was born April 30, 1777 in Brunswick, Germany to a stern father and a loving mother. At a young age, his mother sensed how intelligent her son was and insisted on sending him to school to develop even though his dad displayed much resistance to the idea. The first test of Gauss’ brilliance was at age ten in his arithmetic class when the teacher asked the students to find the sum of all whole numbers 1 to 100. In his mind, Gauss was able to connect that 1+100=101, 2+99=101, and so on, deducing that all 50 pairs of numbers would equal 101. By this logic all Gauss had to do was multiply 50 by 101 and get his answer of 5,050. Gauss was bound to the mathematics field when at the age of 14, Gauss met the Duke of Brunswick. The duke was so astounded by Gauss’ photographic memory that he financially supported him through his studies at Caroline College and other universities afterwards. A major feat that Gauss had while he was enrolled college helped him decide that he wanted to focus on studying mathematics as opposed to languages. Besides his life of math, Gauss also had six children, three with Johanna Osthoff and three with his first deceased wife’s best fri...
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
Throughout the centuries, artists have used the golden ratio in their own creations. An example is “post” by Picasso. When using a golden mean gauge you can see that the lines are spaced to the Golden Proportion.