Geometry Essays

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…

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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…

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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…

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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…

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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…

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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…

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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…

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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…

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Platonic Solids

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…

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