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No, they are not the same, but relate to each other. The medial right triangle of this "golden" pyramid, demonstrated the Pythagorean theorem through the relationship of the two. Ancient Greek mathematicians first studied the golden ratio because of its frequent appearance in geometry. The division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. The Greeks usually attributed discovery of this concept to Pythagoras.
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Are golden mean golden section gold ratio and golden proportion same thing?
Yes They are all the ratio 1.618:1, or (1+51/2)/2:1
What are some modern examples of math that seem to use the same ideas as the ancient greek math?
Pythagorean Theorem would be the first thing to come to mind. Well, this is kind of more related to art/architecture, but there is the golden rectangle and the golden ratio. The golden ratio is represented by the Greek letter phi, which appears as a circle with a slash going through it. It is a value representing the ratio of the lesser to the greater when the ratio of the lesser to the greater is the same as the ratio of the greater to the whole. In Ancient Greek, architects used this technique to create beautiful buildings and works of art, where the ratio of the length to the width of the rectangle in one of the structures (or vice versa) is equal to the golden ratio.
What is one thing mentioned that Pythagoras is known for?
His theorem for a right angle triangle that states the hypotenuse of a right angle triangle when squared is equal to the sum of its squared sides.
What household items have the golden ratio?
A few household things with the golden ratio are a credit card and a student id card. sorry i don't have anything else but I'm doing homework on this so if anyone else has another household thing with the golden ratio i could use some help!
How the Pythagoras theorem is used today?
The Pythagorean theorem is used today for the same thing it was invented for: to describe the relationship between the length of the three sides of a right triangle. Using the Pythagorean theorem, you can find the the length of the third side of a right triangle with two known lengths. This can be useful in a variety of math-based situations, such as when you need to determine the distance between two known points on a graph.
What are three important things Pythagoras did?
Although he is mainly known for hi Pythagoras theorem, his main contribution are the discovery of gunpowder, soon furnishing this int the first musket. although back then it never caught on in the 1600s we found his designs and used them. Also he invented glass in his dicoveries into art and design. And another thing he did was actually discover the shape 'triangle'
Are a theorem and a theory the same thing?
More or less, yes.
Did Isaac newton co create the binomial theorem?
yes Isaac Newton created the binomial theorem
Why is the Fermat's theorem so important today?
It's important as a theorem that's very simple to explain; most school children know Pythagoras's theorem about right angle triangles (a2+ b2 = c2), Fermat proposed that there were no whole number solutions for an + bn = cn for n other than 1 or 2. Fermat wrote in his notebook that he had a "wonderful" proof, but didn't have room to write it down. It was 300 years before it was proved - and for some time it was thought that it might be unprovable. (Gödel's incompleteness theorem states that there are true things that can't be proved true and I was taught that Fermat's might be such a thing).
What is ratio decay?
No such thing as ratio decay. Sorry
Where is the golden apircorn in sou silver?
There is no such thing as a golden apricorn.
Who made pythagorean?
The History of Pythagoras and his Theorem In this section you will learn about the life of Pythagoras and how it is that the theorem is known as the Pythagorean Theorem. Be aware that there are no good records about the life of Pythagoras, so the exact dates and other issues are not known with certainty. In addition, the names of some of the people as well as the places where Pythagoras lived may have different spellings. Pythagoras was born in the island of Samos in ancient Greece1. There is no certainty regarding the exact year when he was born, but it is believed that it was around 570 BC That is about 2,570 years ago! Those were times when a person believed in superstitions and had strong beliefs in gods, spirits, and the mysterious. Religious cults were very popular in those times.Pythagoras of Samos Pythagoras' father's name was Mnesarchus and may have been a Phoenician. His mother's name was Pythais. Mnesarchus made sure that his son would get the best possible education. His first teacher was Pherecydes, and Pythagoras stayed in touch with him until Pherecydes' death. When Pythagoras was about 18 years old he went to the island of Lesbos where he worked and learned from Anaximander, an astronomer and philosopher, and Thales of Miletus, a very wise philosopher and mathematician. Thales had visited Egypt and recommended that Pythagoras go to Egypt. Pythagoras arrived in Egypt around 547 BC when he was 23 years old. He stayed in Egypt for 21 years learning a variety of things including geometry from Egyptian priests . It was probably in Egypt where he learned the theorem that is now called by his name. By the time he was about 55 years old he returned to his native land and started a school on the island of Samos. However, because of the lack of students he decided to move to Croton in the south of Italy. In Croton he started a school which concentrated in the teaching and learning of Mathematics, Music, Philosophy, and Astronomy and their relationship with Religion. It is said that as many as 600 of the worthiest people in the city attended the school, including Theana whom he married when he was 60. The school reached its highest splendor around the year 490 BC. He taught the young to respect their elders and to develop their mind through learning. He emphasized justice based on equality. Calmness and gentleness were principles encouraged at the school. Pythagoreans became known for their close friendships and devotion to each other. More than anyone before him Pythagoras combined the spiritual teachings with the pursuit of knowledge and science. Pythagoras also headed a cult known as the secret brotherhood that worshiped numbers and numerical relationships. They attempted to find mathematical explanations for music, the gods, the cosmos, etc. Pythagoras believed that all relations could be reduced to number relations. At some point Pythagoras was exiled from Croton and had to move to Tarentum. After 16 years he had to move again, this time to Metapontus where he lived four years before he died at the age of 99. Here we have a picture of a statue of Phytagoras in the island of Samos. If you click on the figure you'll be able to see a larger picture. On the bottom of the statue the text is "". The literal translation is "Pythagoras the Samosan", but the preferred translation is "Pythagoras of Samos". Now let's talk a bit about the theorem that bears his name. The Egyptians knew that a triangle with sides 3, 4, and 5 make a 90o angle. As a matter of fact, they had a rope with 12 evenly spaced knots like this one: that they used to build perfect corners in their buildings and pyramids. It is believed that they only knew about the 3, 4, 5 triangle and not the general theorem that applies to all right triangles. The Chinese also knew this theorem. It is attributed to Tschou-Gun who lived in 1100 BC. He knew the characteristics of the right angle. The theorem was also known to the Caldeans and the Babylonians more than a thousand years before Pythagoras. A clay tablet of Babylonian origin was found with the following inscription: "4 is the length and 5 the diagonal. What is the breadth?" So why is it called the Pythagorean Theorem? Even though the theorem was known long before his time, Pythagoras certainly generalized it and made it popular. It was Pythagoras who is attributed with its first geometrical demonstration. That is why it is known as the Pythagorean Theorem. There are hundreds of purely geometric demonstrations as well as an unlimited (that is right -- an infinite number) of algebraic proofs. The Pythagorean Theorem is one of the most important theorems in the whole realm of geometry. We will conclude this section by stating the theorem in words: The square described upon the hypotenuse of a right-angled triangle is equal to the sum of the squares described upon the other two sides. Another way of saying the same thing is:When the two shorter sides in a right triangle are squared and then added, the sum equals the square of the longest side or hypotenuse.
