The Divine Proportion: The Theorem Of Pythagoras

1806 Words4 Pages
bulb-icon

Recommended: About pythagoras

THE DIVINE PROPORTION
"Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold, the second we may name a precious jewel."
--Johannes Kepler Johannes Kepler was one of the most distinguished astronomers and mathematicians. So what was so compelling about a simple relation between two numbers that he effortlessly went ahead to compare one of the most critical theorems of mathematics and this ratio. Throughout his life, Kepler was so fascinated with the Divine Proportion that he wrote several transitions of text on this subject and even fabricated the Kepler's triangle on this basis.
So what is the Divine Proportion ?
In simple terms, two quantities are said to be in the golden ratio/divine proportion if their ratio is the same as the ratio of their sum to the larger of the two quantities. For any two …show more content…

The spiral is visible in hurricanes, seeds, human ears (cochlea), ram's horn, fern leaves, tail of a sea horse, tornadoes, galaxies, whirlpools and so many flowers (sunflowers, daisies, dandelions etc.). This spiral forms a precise mathematical pattern involving the golden ratio. As it gets larger, it retains it's similar form. This form is also known as the "Golden Spiral". Leaves are also generally arranged in this spiral, this can be viewed by looking at the stem directly from above and noting the arc of the stem form one leaf base to the next and the fraction of stem circumference which is inscribed. This pattern ensures that each leaf receives maximum sunlight without crowding out the others. Another reason that It was important to measure the spirals is that it was one of the first instances of the Golden Ratio being found in nature (by Jakob Bernoulli in the 17th

Show More
Related

  • Boundaries, Symmetry and Continuity in Radcliffe's The Mysteries of Udolpho

    1604 Words  | 4 Pages

    Burke, Edmund. "Proportion Further Considered". A Philosophical Inquiry into the Origin of Our Ideas of the Sublime and the Beautiful. New York: P.F. Collier & Son, 1909-1917 (New York: Bartleby.com, 2001). http://www.bartleby.com/24/2/305.html

    Read More

  • Greek Influences on Western Civilization

    340 Words  | 1 Pages

    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.

    Read More

  • Iannis Xenakis Architecture

    1878 Words  | 4 Pages

    This paper will discuss three specific instances: Le Sacrifice, Psappha, and Metastasis. The first principle that I will discuss is the Golden Section. The Golden Section can be found in art and architecture dating as far back as the Parthenon, as well as different places in nature, such as the nautilus shell. The Golden Section is essentially a proportion that is established by taking a single line and dividing that line into two separate sections of unequal lengths, one quite longer than the other.

    Read More

  • Mathematician Research Paper Archimedes

    1008 Words  | 3 Pages

    It is no mystery that without the Ancient Greeks, math as we know it today would not be the same. It is mind blowing to think that people who had no access to our current technology and resources are the ones who came up with the basic principles of the mathematics that we learn and use today without any preceding information on the topic. One of the best examples of such a person is Archimedes. Not only did he excel as a physicist, inventor, engineer, and astronomer, but he is still known today as one of the greatest mathematicians of all time. His contributions to the field laid out many of the basics for what we learn today and his brilliance shocked many. Long after his time, mathematicians were still stumped as to how he reached the genius conclusions that he did. Nicknamed “The Wise One,” Archimedes is a person who can never be forgotten.

    Read More

  • Math and Science of Ancient Greece, India, and China

    2061 Words  | 5 Pages

    "The Foundations of Geometry: From Thales to Euclid." Science and Its Times. Ed. Neil Schlager and Josh Lauer. Vol. 1. Detroit: Gale, 2001. Gale Power Search. Web. 20 Dec. 2013.

    Read More

  • Pythagoras and Plato

    1421 Words  | 3 Pages

    Pythagoras held that an accurate description of reality could only be expressed in mathematical formulae. “Pythagoras is the great-great-grandfather of the view that the totality of reality can be expressed in terms of mathematical laws” (Palmer 25). Based off of his discovery of a correspondence between harmonious sounds and mathematical ratios, Pythagoras deduced “the music of the spheres”. The music of the spheres was his belief that there was a mathematical harmony in the universe. This was based off of his serendipitous discovery of a correspondence between harmonious sounds and mathematical ratios. Pythagoras’ philosophical speculations follow two metaphysical ideals. First, the universe has an underlying mathematical structure. Secondly the force organizing the cosmos is harmony, not chaos or coincidence (Tubbs 2). The founder of a brotherhood of spiritual seekers Pythagoras was the mo...

    Read More

  • An Extended Definition of Beauty

    1058 Words  | 3 Pages

    To begin, the concept of unity follows the Aristotelian proposition that nothing can be added to or taken away from a perfect work of art. Next, proportion, or the harmony of the parts to the whole and to each other is, based the mathematical and geometric relationships discovered by the Ancient Greeks. Finally, clarity refers to the logical quality of design, as well as the luminosity of coloration. Therefore, St. Thomas explains that beauty is intimately tied to knowledge, and that we form our judgments according to what pleases us.

    Read More

  • Pythagoras: The Foolish Genius

    670 Words  | 2 Pages

    Pythagoras, a man who is immortalized through his genius in the field of mathematics, or more specifically and more widely known the Pythagoras Theorem. A revolutionary theorem, which he created alone, which allows one to uncover the length of the missing side of a triangle by utilizing the other two sides. However, this theorem was not the only thing that Pythagoras was remembered for. In fact he is remembered for his philosophies, childhood, secret life and society, and influential adventures. The man, Pythagoras, was so famous in his time he was able to build and keep his own religious secret society, which has made it difficult to find detailed descriptions on Pythagoras’ life.

    Read More

  • Fabulous Fibonacci

    1233 Words  | 3 Pages

    One of the most common places to see Fibonacci numbers is in the growth patterns of plants. Growth spirals are characterized by both a circular motion, and elongation. As a branch grows, it produces leaves at regular intervals, but not after each complete circle of its spiral. The reason the leaves are not directly above each other is because all of the leaves would not be able to get the necessary elements. It appears that leaves are generated on the stem in phyllotactic ratios where the numerator and denominator are both Fibonacci numbers. The numerator is the number of turns, and the denominator is the number of leaves past until there is a leaf directly above the original. The number of leaves past, ad both directions of turns produce 3 consecutive Fibonacci numbers. For example, in the top plant on this transparency, there are 3 clockwise rotations before there is a leaf directly above the first leaf, passing 5 leaves along the way. Notice that 2, 3, and 5 are all consecutive Fibonacci numbers. The same is true for the bottom plant, except that it rakes 5 rotations for 8 leaves. We would write this as 3/5 clockwise rotations per leaf on the top one and 5/8 for the bottom. Although, these are just computer-generated plants, the same is true in real life. A few real life examples of these phyllotactic ratios are 2/3 elm, 1/3 black berry, 2/5 apple, 3/8 weeping willow, and 5/13 *censored* willow. Daisies display Fibonacci numbers in their own unique way. If we look at this enlarged seed head of a daisy, and took the time to count the number of seeds spiraling in clockwise and counter clockwise rotations we would arrive at 34 and 55. Note that these are consecutive Fibonacci numbers. Many other flowers e...

    Read More

  • Essay On Golden Ratio

    1406 Words  | 3 Pages

    A rectangle is a very common shape. There are rectangles everywhere, and some of the dimensions of these rectangles are more impressive to look at then others. The reason for this, is that the rectangles that are pleasing to look at, are in the golden ratio. The Golden Ratio is one of the most mysterious and magnificent numbers/ratios in all of math. The Golden Ratio appears almost everywhere you look, yet not everyone has ever heard about it. The Golden Ratio is a special number that is equal to 1.618. An American mathematician named Mark Barr, presented the ratio using the Greek symbol “Φ”. It has been discovered in many places, such as art, architectures, humans, and plants. The Golden Ratio, also known as Phi, was used by ancient mathematicians in Egypt, about 3 thousand years ago. It is extraordinary that one simple ratio has affected and designed most of the world. In math, the golden ratio is when two quantities ratio is same as the ratio of their sum to the larger of the two quantities. The Golden Ratio is also know as the Golden Rectangle. In a Golden Rectangle, you can take out a square and then a smaller version of the same rectangle will remain. You can continue doing this, and a spiral will eventually appear. The Golden Rectangle is a very important and unique shape in math. Ancient artists, mathematicians, and architects thought that this ratio was the most pleasing ratio to look at. In the designing of buildings, sculptures or paintings, artists would make sure they used this ratio. There are so many components and interesting things about the Golden Ratio, and in the following essay it will cover the occurrences of the ratio in the world, the relationships, applications, and the construction of the ratio. (add ...

    Read More

  • Binomial Theorem Essay

    1796 Words  | 4 Pages

    Then in Euclid II, 7, it goes farther to explain that “if a straight line be cut at random, the square on the whole and that on one of the segments both together, are equal to twice the rectangle contained by the whole and said segm...

    Read More

  • Essay on Number Theory

    1699 Words  | 4 Pages

    ...its relation to the Golden Angle, which appears in the primordia of plants in order to give the maximum number of primordia for plants. I like to think of an idea in the book, ?Life?s Other Secret,? which says that it?s not just Fibonacci Numbers that matter; it?s also the matter in which they arise (Stewart).

    Read More

  • The History of Math

    810 Words  | 2 Pages

    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...

    Read More

  • Golden Ratio

    538 Words  | 2 Pages

    The golden ratio is a term used to describe proportioning in a piece. In a work of art or architecture, if one maintained a ratio of small elements to larger elements that was the same as the ratio of larger elements to the whole, the end result was pleasing to the eye.

    Read More

  • Essay On Euclid

    681 Words  | 2 Pages

    Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.

    Read More

More about The Divine Proportion: The Theorem Of Pythagoras

Open Document