Algebraic geometry

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.…

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…

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 with the solutions of polynomial equations , algebraic numbers , algebraic extension or algebraic expression. It AGREES distinguishes between : Elementary algebra is the part of algebra that is usually taught in…

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…