Algebraic geometry

The aim of this task is to investigate geometric shapes, which lead to special numbers. The simplest example of these are square numbers, such as 1, 4, 9, 16, which can be represented by squares of side 1, 2, 3, and 4. Triangular numbers are defined as “the number of dots in an equilateral triangle uniformly filled with dots”. The sequence of triangular numbers are derived from all natural numbers and zero, if the following number is always added to the previous as shown below, a triangular number

axioms and proved them. Greek mathematics refers to the time between 600 B.C to 529 A.D. Most of the mathematical work done by the Greeks was geometry. It is said to have started with Thales, a famous Greek mathematician, who was the first person to lay down the abstract development of geometry. He established what is known as Thales Theorem. Thales used geometry to calculate the height of pyramids and find the distance from ships to shore. However, some say that Pythagoras deserves the true title for

mathematics and made many contributions to geometry. Not much is known about the early life of Pythagoras. However, it is known that his father, Mnesarchus, was a merchant and that Pythagoras traveled frequently with his father (“Pythagoras of Samos,” n.d.). Thales and Anaximander were philosophers who are believed to have influenced Pythagoras and his interest in mathematics (“Pythagoras of Samos,” n.d.). In fact, Anaximander was interested in geometry. He lectured on Miletus where Pythagoras

1. Write a short (2 pages) essay on Greek Mathematics The mathematicians of ancient Greece contributed to the Mathematic of the world, and its applications vary on an intellectual basis, from geometry to engineering, astronomy to design. Influenced by the Egypt mathematicians, Greek mathematicians made breakthroughs such as Pythagoras' theory of right-angled triangles. Their Mathematic created the basic mathematical building blocks, and being useful up to today for mathematicians and scientists.

They had passed down their system of mathematics to the ancient Babylonians. In 498 AD, the Indian (Hindu) mathematician and astronomer Aryabhatta introduced the decimal system when he stated, “Sthanam sthanam dasha gunam.” This statement means, “place to place in ten times in value.” This may have been the origin of the modern ten-based decimal value system used today. The ten number based system used with the Hindu decimal zero was adopted by Arabian mathematicians. They had further modified

Escher’s full name is Maurits Cornelis Escher. He was born on June 17, 1898, in Leeuwarden, Netherlands. When he was five years old he took up carpentry and piano lessons until the age of 13. When he attended highschool he was an excellent drawer but received poorer grades in most other subjects. He went to Haarlem School of Architecture and Decorative Arts where he studied architecture for a short while before moving onto decorative arts. Having gained experience in drawing and woodcutting in particular

Angular shaped often signifies that it is from another plane or sphere of being. Animal shaped can often be the person’s spirit animal or an attitude they are putting off that is similar to that particular animal. Shamanic people sometimes shift auras, showing off their spirit animal instinctively. Atoms floating away from the aura shows a lack of determination and self, discipline. They want everyone to know how they feel and feel it too, so they are putting it out there for everyone to see

Anyone who has ever encountered a circle in math class has faced the issue of finding the circumference and area, or both, of that circle. Additionally, anyone who has attempted to accomplish that task has come into contact with Pi, denoted by the Greek letter π. Pi, pronounced “pie,” represents the ratio of the circumference of a circle to its diameter and has a numerical value of 3.14159… Simple enough. Now, we are introduced to τ, or “tau”, which connects the circumference of a circle to its radius

Petersburg Academy. Not only did he study mathematics, but made some large advancements in astrology, mechanics and music. Although trigonometry, geometry and calculus were his main subjects of focus. Leonhard Euler was the one who created and first used the f(x) that is almost always used when writing equations and formulas. He also originated the ‘e’ base that is used in modern notation of natural

tessellation are thousands of dots and lines. This drawing is a mezzotint which is made by hatching, layering lines and dots. The mathematics behind this certain tessellation can get pretty complicated. Escher’s work mainly involves the mathematics of the geometry of space and planes. In this tessellation, it is evident how the planes change as the lizards go into the tessellation and leave. “Lizards” would be classified as an irregular tessellation, something that Escher was very interested in, where the