Euclidean geometry

Maurits Cornelis Escher, also known as M.C Escher, was a graphic artist between 1898 and 1972. He is most famous for his unique works that incorporated mathematics, specifically the manipulation of perspective and space. He developed an innovative style of both print and engraved art (“M.C. Escher Biography”). Some of his most well-known works include, “Relativity,” “Ascending and Descending,” “Hand with Reflecting Sphere,” and “Metamorphosis” (Gallery, “Most Popular”). M.C. Escher was born…

Over time, the Greek civilization has had many different and unique inventions. However, Greek Geometry was one of the most crucial inventions ever discovered. Geometry helped to find out precise measurements, construct advanced architecture, and become the leading civilization in mathematics. The invention was discovered by a mathematician named Euclid. He had many math theorems of his own, and later wrote his own book. The Elements contained all the works from previous Greek mathematicians,…

1. During group time, T along with the rest of his group were given the instructions by the gym teacher. She said, “I want you to see how many pull ups you can do. Don’t stop when you begin feeling pain, try and see if you can hold it a little longer.” T was the first person in his group to go. Before T went up to the bar, he turned his head half way to the side, just for his friend to see his face. He smirked and then quickly turned his head around and leaped toward the bar. The teacher asked T…

The mission of Julia Robinson Mathematics Festival activities is to pique students' interest in mathematics and problem solving. We also strive to open the minds of students who find math hard, tedious, and not useful. The Julia Robinson Mathematics Festival was founded in 2007 by Nancy Blachman to provide intellectual stimulation and to enable students to have fun exploring and making mathematical discoveries. What Happens at at Festival The Julia Robinson Mathematics Festival is a hands-on…

Introduction The NAPLAN test (http://www.nap.edu.au) is for both primary and secondary schools to assess the performance of Australian students against minimum national standards (Reys et al., 2012). With this in mind the approach to answering the questions was to work through all parts of the questions just like a student would, to form an understanding of the process and methods a student taking the test would perform. The questions were not overly difficult to conceptualise, however, working…

Compasses and straightedges are tools used regularly in geometry. Compasses are used to draw precise circles and arcs, leading to making many geometric figures. Straightedges are used to make straight lines that are exact measurements. There is a need for students to understand and be able to construct geometric figures using a compass and straightedge. This is because students will be able to understand the steps it takes to construct geometric figures, it allows students to understand how to…

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…

Then formula is cosα=b/c=(adjacent leg)/hypotenuse Here is also a diagram for easier understanding. The Law of cosines The law of cosine first appears in Euclid’s Elements, which is one of the very first textbook of geometry. If we got a triangle ABC and if angle β is an acute angle then we use the following formula to calculate sides: We can use the law of cosines in a triangle to calculate angles and sides of triangle. For that to happen we must already know two sides…

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.…