Geometry

Degenerate Cases of Conic Sections: Conics are formed when a plane and a double cone intersect. These intersections can form a variety of conics. These include: circles, parabolas, ellipses and hyperbolas. A circle can be formed from a cone if a plane intersects with the cone at an angle perpendicular to the base of the cone. This circle is also formed by the equation: (x-h)2+ (y-k)2=r2. This equation creates a relation because the collection of points does not pass the vertical line test. To…

If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…

Famous philosopher Thales once said, “The most difficult thing in life is to know yourself.”, meaning it takes a while to fully understand one’s self and the strengths or weaknesses within (“Thales”). Thales is an ancient Greek philosopher born in the city of Miletus (“Thales of Miletus” Science). Although, he was a Milesian, his parents, Examyes and Cleobuline, were Phoenicians themselves (“Thales of Miletus” Science). Very little was known about Thales, such as his exact birth and death…

Is Algebra Necessary? By The New York Times Algebra is necessary because it is the branch of mathematics that studies l combining elements of abstract structures according to certain rules . Originally these elements would put be interpreted as numbers or quantities, so that the algebra somewhat originally was a generalization . The adjective " algebraic " usually denotes a relationship with algebra , such as in algebraic structure . For historical reasons, it may also indicate a relationship…

The history of Calculus can be traced back as early as the 5th Century B.C.E. in Ancient Greece. The first major discovery was made by a Greek scholar named Hippasus. Not much is known about this philosopher who studied under Pythagoras; but, he has sometimes been credited with the discovery of irrational numbers. \begin{center} \includegraphics[width = 6 cm]{triangle.png} \end{center} He described his reasoning as: \begin{enumerate} \item Start with an isosceles right triangle with side…

Students need to understand and be able to construct geometric figures using a compass and straightedge. I chose argument A because students need to learn the usage of primary instruments before they enhance to the advanced exercises online, and in order to understand the information you must learn how to actually use it with your hands, if they are not capable to use a simple tool they wouldn't be able to use the complex ones. In math, a compass is a tool that’s used to measure line segments…

Sacred geometry connects natural patterns, designs, and structures to an overall sacred origin. This inseparable relationship between complex solidified values and generalized faithful concepts appears to be the unlikeliest duo. This mysterious relationship proved to be a huge attraction to many mathematicians, including Plato, Carl Friedrich Gauss, Leonardo da Vinci, and Johannes Kepler. However mathematicians today continue to seek evidence that complies with Plato’s cosmology, and “theory of…

Research shows that Hypatia of Alexandria was one of the first women to make substantial contribution to the development of mathematics. She lived in the great center of ancient learning; Alexandria, Egypt, in the 4th century A.D. While it t is assumed that she studied mathematics under her father, Thon of Alexandria; it is known that she was the head of the Platonist school in Alexandria around 400 A.D. Hypatia contributed in many ways to math; it is said that she edited the work on “The Conics…

Born on April 15, 1707 in Bales, Switzerland was man names Leonhard Euler. Following in his father's footsteps he was studying to be a rural clergyman. “Though originally slated for a career as a rural clergyman, Euler showed an early aptitude and propensity for mathematics, and thus, after studying with Johan Bernoulli, he attended the University of Basel and earned his master's during his teens.”(Biography.com Editors) During his time at school, Euler found a passion for mathematics. “By 1726,…

Pythagoras Born: about 569 BC in Samos, Ionia Died: about 475 BC He is named the first mathematician. Pythagoras was born near the Ionian coast of the Mediterranean, in the rich merchant family. After living in Egypt for 22 years and in Babylon for 12 years, he gained deep knowledge in natural and mathematical sciences. He gathered around a group of like-minded people, mostly aristocrats, and created a secret circle. The members of the circle studied various issues of philosophy and mathematics.…