Projective geometry

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…

allows students to be creative and get-along together. I think it would be a great learning experience for students because it allows them to experience the life of those slaves who could not read or write. It allows them to appreciate history, geometry, quilts, and geology. I think it encourages them to reason and think critically. The article made me realize that quilts are just for decorations but that they are part of history. I do not think many people know the importance of quilts.…

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…

think they should 've kept math they way they did before they implemented the new way of learning. And that 's why I hate math and dread going to math class” says Patrick Murzinski, an honors math student. Joey Rorro, a former honors geometry student states, “I hate geometry. Its useless information unless you are pursuing a career in architecture. Trying to find the tangent of an angle is next to white ink as the most useless thing the world has ever seen.” Just like what Patrick said, the…

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…

Integrals have been around for hundreds of years and have been used in several ways to solve complicated math problems. An integral is a function that expresses the area under the curve of a graph of a function. The first time the technique was brought forward was by a greek astronomer Eudoxus in the 370 BC. He used the technique called as the method of exhaustion which helped him find area or volume. The way he achieved this was using infinite numbers of division. Later Archimedes came along…

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…

Math has many significant aspects. However, it wasn’t until I was assigned this assignment, that I fully understood the wide variety mathematics encompasses. Math has a specific part called Geometry, it is this section that I am going to mainly focus on. Geometry consists of shapes. These many shapes can then be put together to form patterns. They are the Golden Ratio, Fractals, Spiral Growth, and Voronoi Patterns. The Golden Ratio consists of ratios which the two larger sums are equivalent to…

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…

compared to what it should be in order to start finding a diagnosis. Lastly, doctors use math to calculate just how broken a patient might be. In “ How CAT scans work,” the author demonstrates how the doctor uses different forms of math such as geometry and trigonometry to find dimensions in x-rays. doctors use trigonometry especially to find just at what angle the X-ray needs to be captured in order to see what damage has been done. In conclusion, being a doctor includes tons of math.…