Parabola and Focus

A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The locus of points in that plane that are equidistant from both the directrix and the focus is the parabola. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a planewhich is parallel to another…

Conic Section

AN INTRODUCTION TO CONIC SECTIONS There exists a certain group of curves called Conic Sections that are conceptually kin in several astonishing ways. Each member of this group has a certain shape, and can be classified appropriately: as either a circle, an ellipse, a parabola, or a hyperbola. The term “Conic Section” can be applied to any one of these curves, and the study of one curve is not essential to the study of another. However, their correlation to each other is one of the more intriguing coincidences of mathematics. A CONIC SECTION DEFINITION Put simply, a conic section is a shape generated when a cone intersects with a plane. There are four main types of conic sections: parabola, hyperbola,…

Elementary Math Method: Measurement and Geometry

Navigating through the Teachers’Lab website section on shape and space in geometry was very easy and quite enjoyable; it would appeal to students because of its color and interaction. The quilt activity, based on symmetry, is particularly useful for students who are visual and kinesic learners. I did not discover anything about symmetry I did not already know but the idea of naming the types of symmetry with letters of the alphabet was a novel innovation for me. Four types of symmetry are explored and named with a letter of the alphabet in accordance to the direction of symmetry; for example, symmetry that is both horizontal and vertical is called H-symmetry; symmetry that is horizontal (left to right, right to…

Tessellation Patterns

A tessellation is “the filling of a plane with repetitions of figures in such a way that no figures overlap and that there are no gaps” (Billstein, Libeskind, & Lott, 2010) . Tessellations can be created with a variety of figures, including triangles, squares, trapezoids, parallelograms, or hexagons. Tessellations use forms of transformations to show the repetitions of the figures. The transformations can includes translations, rotations, reflections or glided reflections. Any student would be able to create their own original tessellation by piecing together a variety of geometric shapes in a repetitive pattern by a transformation, either by hand or on a computer. The tessellation that I have created includes hexagons, squares, and triangles. I placed the squares and triangles…

Pythagorean Quadratic

The Pythagorean Theorem was termed after Pythagoras, who was a well-known Greek philosopher and mathematician, and the Pythagorean Theorem is one of the first theorems identified in ancient civilizations. “The Pythagorean theorem says that in any right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse” (Dugopolski, 2012, p. 366 para. 8). For this reason, many builders from various times throughout history have used this theorem to assure that their foundations were laid out with right angles. In this assignment, we will use the example of locating a treasure using two different treasure maps as the two points needed to determine how many paces it will…

Platonic Solids Essay

I think that there are exactly five regular polyhedra, and I intend to prove why there are exactly five polyhedra. Ok, firstly, we need to identify what the five polyhedra are. They are the tetrahedron, the cube, the octahedron, the icosahedron, and the dodecahedron. All of these are regular polyhedra have something in common. For each shape, each of its faces are the same regular polygon, and the same number of faces meet at a vertex. This is the rule for forming regular polyhedra. Now we need to analyze the shapes of the faces, and the number of them meeting at a vertex. The faces for the tetrahedron, octahedron, and the icosahedron are all triangles, and the number of faces…

Guido Fubini

Guido Fubini, A famous mathematician, was born January 19th 1987 in Venice, Italy. His father, Lazzaro Fubini, was a mathematics teacher so he came from a mathematical background. Guido was influenced by his father towards mathematics when he was young. He attended secondary school in Venice where he showed that he was brilliant in mathematics. It was then clear that from this stage he would follow this career. In 1896 Guido entered the Scuola Normale Superiore di Pisa. There he was taught by Dini and Bianchi, who quickly influenced Guido to undertake research in geometry. He presented his doctoral thesis Clifford’s Parallelism in Elliptic Spaces in 1900. Most young doctoral students take a few years to make themselves well know…

Physics lab report-motion

Introduction A toy company is now making an instructional videotape on how to predict the position. Therefore, in order to make the prediction accurate, how the horizontal and vertical components of a ball’s position as it flies through the air should be understood. This experiment is to calculate functions to represent the horizontal and vertical positions of a ball. It does so by measuring and calculating the components of the position and velocity of the ball during the toss. Therefore, we can also calculate the acceleration during the procedure. Prediction The x-axis is located on the ground level horizontally, pointing to where the ball is initially thrown, that is opposite the direction the ball flies. The vertical y-axis passes through…

Reflective Paper

Mathematics for Elementary Teachers is a two- part course designed to prepare potential educators the mathematical concepts need to teach to elementary schools students K-8. The two-part course also addresses the relationship concepts to the National Council of Teachers of Mathematics Standards for K-8 instruction (Billstein, Libeskind & Lott, 2010). This semester, which presented the second half the two-part course, the MTH/157 curriculum gave appropriate statistical methods to analysis data, applied basic concepts of probability, applied and identified geometric figures and shapes for problem solving, and identified applications of measurements. This class introduced very interesting, exciting and fun ways how to teach the above mathematical concepts like probability in the form of games. There are several types of probabilities: Theoretical…

Geometry: Indifference Curve, Budget Line, Equilibrium of Consumer

Research the Following: 1. Indifference Curve – An indifference curve is a graph showing combination of two goods that give the consumer equal satisfaction and utility. Definition: An indifference curve is a graph showing combination of two goods that give the consumer equal satisfaction and utility. Each point on an indifference curve indicates that a consumer is indifferent between the two and all points give him the same utility. Description: Graphically, the indifference curve is drawn as a downward sloping convex to the origin. The graph shows a combination of two goods that the consumer consumes. The above diagram shows the U indifference curve showing bundles of goods A and B. To the consumer, bundle A and B are the…

Two Variable Inequality

This week we are learning about two-variable inequalities as they pertain to algebraic expressions. The inequality can be graphed to show the values included in and excluded from a given range of numbers. Solving for inequalities such as these is a critical skill in many trades which can save or cost a company a lot of time and money. Ozark Furniture Company can obtain at most 3000 board feet of maple lumber for making its classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. Write an inequality that limits the possible number of maple rockers of each type that can be made, and…