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Geometry

2 pages (500 words)

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...Geometry Geometry is a branch of mathematics that deals or attempts to explain and describe the shape, size, or relative position of an object in space. The study of geometry dates back to the time of ancient Greek. The Euclidian geometry for example originated in the 6th century and it laid the foundation for modern geometry. Currently, the study has advanced to include other branches of mathematics such as number theory, algebra, and topology. Riemannian geometry for example is among the latest braches of geometry. Each of the above fields of specialization has a...

Geometry

1 pages (250 words)

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...Geometry - Pythagorean Triples A Pythagorean triple indicates that the relations between three positive integers a, b and c leads to the formation ofa right angled triangle in such a manner that;
a2 + b2 = c2
Where a, b and c indicates the three sides of the right angled triangle (as in the fig)
The equation holds good for sets of three integers known as triples. Since the equation is based on Pythagorean Theorem, hence the name Pythagorean triples. A well known example of such a triple is (3, 4, 5). This implies that 32+42=52
Other such examples are (5, 12, 13), (7, 24, 25), (8, 15, 17) etc. Euclid's formula proves quite helpful in generating a series of such triples....

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College Geometry - neutral geometry and Euclidean geometry

3 pages (750 words)

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...GEOMETRY Introduction Geometry is a branch of measure mathematics that revolves in and around size, shape, relative figure’s position, together with properties of space. It is one of the oldest branches of mathematics that originated from the ancient Greek among the mathematics scientists. Initially, it dealt with areas, volumes, and lengths but in the 3 BC, geometry took a new path as a result of efforts from Mathematicians such as Euclid with his Euclidean geometry. He laid down the foundation of today's geometry; absolute geometry is type of geometry that has developed...

Fractal Geometry

2 pages (500 words)

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...Geometry Fractal geometry is rather new mathematical theory which is completely different from the traditional concepts of Euclidean Geometry. Fractal geometry describes elf-similar or scale symmetric objects. It means that if to magnify these objects, their parts will bear an exact resemblance to the whole object. The word "fractal" was created by Benoit Mandelbrot and it means "to break", whereas the form of adjective "fractus" means "fragmentated". (Brandt 24)
It is a matter of fact that the word "fractal" has two definite meanings: the first meaning refer to colloquial use and the second is connected with geometry. In colloquial speech fractal is a shape which is self-similar... or...

Geometry proj2

4 pages (1000 words)

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...Geometry 2 (MTHH 036 058) Part A: Other Transformations (24 points Draw XYZ with vertices X(0, 3), Y(2, 0) and Z(4,2). Draw XYZ and its reflection image in the line x = 4. Make sure to label the new triangle at X’Y’Z’. (3 points)
2. Draw XYZ with vertices X(1, 2), Y(0, 5), and Z(-8, 0). Graph XYZ and its image after a 270 rotation about the origin. Name the coordinates of each vertex of the image. (3 points)
3. You are making hand shadows on a wall using a flashlight. You hold your hand 1 foot from the flashlight and 5 feet from the wall. Your hand is parallel to the wall. If the measure from your thumb to ring finger is 4 inches, what will be the distance... Project 2 Evaluation 32...

Triangulation in Geometry

12 pages (3000 words)

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...geometry Outline Key definitions 2. Euler's theorem 3. Discovering and generalizations 4. Gauss-Bonnet theorem 5. Surfaces, theirs topology and triangulation
1. Key definitions
To make our considerations of extensions of the Euler's theorem and triangulation concepts more pure, we need to preliminary define the key notions from the related topics.
First of all, polygon is a closed plane figure with sides (Weisstein 2002). Then, a polyhedron is the union of a finite set of polygons such that: (i) any pair of polygons meets only at their sides or corners; (ii) each side of each polygon meets exactly one other polygon along an edge; (iii) it is possible to travel from the interior... Triangulation in...

Geometry Task 3

2 pages (500 words)

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...Geometry the Easy Way. APPLYING CONGRUENT TRIANGKS, 7,109-111.
Theorems for congruent Triangles. Methods for proving triangles to be congruent. ... 07 Feb. 2008 ASSIGNMENT INSTRUCTIONS ment: If the base angles of a triangle are congruent, then the triangle is isosceles. Drawing:
ABC is a triangle with vertex A, B, C and ABC = ACB
Given:
Angle ABC= ANGLE ACB.
Constructed:
Draw a line AM such that it is perpendicular to BC and passing through the vertex A.
Prove:
The Triangle is isosceles, that is,
AB = AC
PROOF:
From triangles ABM and ACM,
Angle AMB= Angle AMC= Right Angle
...

Geometry

1 pages (250 words)

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...Step Draw a line AB that we will be divided into 3 (in this case) equal parts. From point A, draw a line segment at an angle to the given line, and about the same length. The exact length is not important.
Set the compasses on A, and set its width to a bit less than one third of the length of the new line.
Step the compasses along the line, marking off 3 arcs. Label the last one C.
With the compasses width set to CB, draw an arc from A just below it.
With the compasses width set to AC, draw an arc from B crossing the one drawn in step 4. This intersection is point D.
Draw a line from D to B.
Using the same compasses width as used to step along AC, step the compasses from D along DB making 3... Draw a...

Geometry

7 pages (1750 words)

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...Quantitative Literacy Steve Beckman WGU QLT1 Task September29, A. Complete the following graphs:
1. Graph the following values on a single number line
• Value 1: 1
• Value 2: 0
• Value 3: –6
• Value 4: 3/4
• Value 5: –1.7
2. Graph the following points on a single coordinate plane. Make sure to indicate labels for each quadrant of the coordinate plane.
• Point 1: (3, –2)
• Point 2: (0, 0)
• Point 3: (–1, 7)
• Point 4: (3, 5)
• Point 5: (–4, –5)
(3) Graph the following functions on a separate coordinate planes.
Function 1: y = 2x - 1
y
Function 2: y = (-3/4)*x + 5
y... Literacy Steve...

The History of Projective Geometry

3 pages (750 words)

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...Geometry Introduction Projective geometry is the aspects of mathematical studies that had to do with the study of relationships existing between geometric figures and the mappings or images that are brought into existence as a result of the projection of these geometric figures on some other surface. The focus of the projective geometry is the geometric aspects and properties that are affiliated to changes of perspectives. To put it in simple words, projective geometry delves on geometrical aspects like concurrence and co- linearity and ignores properties like distances and angles. In the everyday life, one often does come across varied aspects... of the of the Concerned 2 May The History of Projective...

BIOMETRICS: Hand Geometry and Vein Check

2 pages (500 words)

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...Geometry and Vein Check Hand Geometry and Vein Check of the Technology Hand geometry is a technology that measures and records the length, width, and surface area of a person’s hand. A plate with five pegs and a camera are used in capturing the silhouette image of the hand. Once the image is captured, up to “31,000 points are analyzed and 90 measurements taken; the measurements range from the length of the fingers, to the distance between knuckles, to the height or thickness of the hand and fingers” (NSTC, 2006, p. 8).
(360 Biometrics, 2011)
Unlike the hand geometry, vein geometry is a fairly recent...

E-Learning/Geometry Shapes Lesson/Blog Entries

4 pages (1000 words)

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...Geometry Shapes Lesson/Blog Entries E-Learning principles and E-Learning role to promote critical thinking skills E-Learning is the learning or teaching process that is done by the use of electronic media. This term is specifically used in the educational field. The learning process that is executed in a class or outside the class by the use of electronic technology is termed as E-learning. Today, e-learning is being implemented in every country of the world because of the educational advancements; it has become the necessity of students to use technology and electronic media as a part of their studies. In most of the schools, e-learning is included in the curriculum. Basically, e... ?E-Learning/Geometry ...

Fractal Geometry Relating To Dance and Leaves

6 pages (1500 words)

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...Geometry Relating To Dance and Leaves Thematically, this paper explores somemathematical concepts, which possesses aesthetic appeal and captures the ways through which mathematical aesthetic shapes nature and art that result in expression of human response to such forms. In other words, fractals is a geometrical or physical structure having irregular or fragmented shape at all measurements levels between the largest as well as the smallest measurement, which include certain mathematical or physical structure, the perimeter that relate to a curve being greater than the spatial dimensions. Euclidean Geometry tries to study flat space. This can be illustrated by geometrical concepts using... Fractal...

Teaching Geometry with technology in middle OR high school

13 pages (3250 words)

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...Geometry with technology in middle OR high school xxxxx School: xxxxx xxxxx xxxxx Due xxxxx Introduction
Technology has become an institutional tool at all educational levels. The use of computers as well as advance form of calculators has changed the way mathematics is taught. According to a research the engagement of young students in the class has generally increased with the use of technology. As a result, this has increased their level of interest towards their studies. In order to make students more attentive and alert in the mathematics class the best way is to teach the difficult part of the course like geometry with technology (Liskom, 2008).
Mathematics is a type of reasoning. When...

Why Geometry has played a central part in Painting

14 pages (3500 words)

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...geometry has played a central part in Painting (College) What, really, is geometry? How do we perceive and understand the meaning of it and its place in Art? By using ‘Kosuthian’ method of explanation, the definition of Geometry is ‘the branch of mathematics concerned with points, lines, curves, and surfaces (In Greek geometrein means to measure the land). In addition, we could also add some key words, which are mainly associated with this discipline: shape, form, pattern, symmetry, balance, scale, system, proportion, structure, repetition. Most of the terminology we find in art and math, and obvious connection between the two of them is...

Mapping and The Geometry of Form and Function of Cities

20 pages (5000 words)

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...GEOMETRY OF FORM AND FUNCTION OF CITIES The paper analyses the fractal nature of cities for having a deeper understanding of urban density and determinism. Additionally, the aspects of urban boundaries, urban morphology, connectivity, and transportation, node points of the city and hierarchy of connections are discussed in the paper. TABLE OF CONTENTS Introduction 4 Definition and Measurement of Urban Shapes 6 Measurement of Urban Morphology 7 Hierarchy of Connections 11 Mapping, Connectivity And Transportation Within The City 12 Human Activity Towards Different Node Points Via The City 13 Shape, Complexity And Forms Of Cities 14 Urban Design Strategy for the City of Derby... ……………………….16...

An essay about the history, orgin, and use of pi( symbol used in geometry)

4 pages (1000 words)

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...geometry, the constant pi shows the relationship that exists between the circumference and diameter of a circle, regardless of its size. This constant remains the same regardless of the size of the circle. So, π = C/d serves as the basic relationship. Further modification can also help to rewrite the relationship as π = C/r2. The number is also transcendental; it is a number... and Section # of A helping of pi, anyone? From being called an Archimedes’ Constant to becoming the modern day “pi”, π has certainly come a long way. For the purpose of simplicity, the word “pi” will be used to refer to this wonderful irrational number, the serves as an object of fascination for both mathematicians and...

Written above the door of Platos academy was the inscription: Let no one unversed in geometry enter here. Why is mathematics so crucial for philosophical tra

10 pages (2500 words)

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...geometry enter here”. Why is mathematics so crucial for philosophical training according
to Plato?
Plato – one of the most important educational theorists and curriculum developers in Western history, whose contribution to the theory and practice of mathematics education has had a profound impact over the ages, possessed educational interests and accomplishments founded on the grounds of mathematical education based upon proofs and facts. The entrance to the Academy he established in Athens, famously announced:
“Let no one ignorant of geometry enters here.”
- inscription above Plato’s Academy (Q1)
Some... of the admiring features of Plato’s Academy were:
Tuition Free: The students of the...

Chaos theory Applications to PDEs (geometry design)

8 pages (2000 words)
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...?Application of Chaos Theory in the Differential Equations Application of Chaos Theory in the Differential Equations Introduction The chaos theory in the finite dimensional dynamical systems is known to exist and it includes or leads to the development of discrete systems and maps of the ordinary differential equations. This theory has led to profound mathematical theorems that have numerous applications in different fields including chemistry, biology, physics, and engineering among other fields or professions (Wasow, 2002). However, the chaos theory of the partial differential equations has never been well-developed (Jordan and Smith, 2003; p. 55). Therefore, there has been a growing... of Chaos...

Chaos theory Applications to PDEs (geometry design)

8 pages (2000 words)

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...Application of Chaos Theory in the Differential Equations Application of Chaos Theory in the Differential Equations Introduction Thechaos theory in the finite dimensional dynamical systems is known to exist and it includes or leads to the development of discrete systems and maps of the ordinary differential equations. This theory has led to profound mathematical theorems that have numerous applications in different fields including chemistry, biology, physics, and engineering among other fields or professions (Wasow, 2002). However, the chaos theory of the partial differential equations has never been well-developed (Jordan and Smith, 2003; p. 55). Therefore, there has been a growing demand... of Chaos...

Write about the reasons of the need of geometry who Descartes and Fermat contributed founding it. Also write about if there was a rivalry between them If there was, what caused it

1 pages (250 words)

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...Geometry A number of Fermats first innovative mathematics comes into view to inspire by a famous complexity of Apollonius. In addition, decisive problem was this if from an end in a plane four-fixed appearance are drained and four additional lines through a point P traverse the initial four, the entire at the identified angle. It should be noted that if the distance next to the four changeable lines from P to wherever they traverse the others is identified as a, b, c, as well as d; then if a · c is in stable ratio to b · d, the position P moves on a conic segment. A theorem that is not simple to write more pithily in simple language called the four-line theorem. In...

On the geometry of piecewise circular curves T.F.Banchoff and P.J.Giblin, American Mathematical Monthly, (101),1994,403-416, In the plane a smooth piecewise circular curve is a curve made from arcs of circles such that at points where two arcs join the

6 pages (1500 words)

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...geometry of objects or a combination of objects. These can be created by a person through a graphic user interface (GUI) or by the application of software through an application programming interface (API).
Given the huge demand... for efficient geometric modeling systems, solid modeling systems or solid modelers therefore need to be more versatile than ever before to be able to represent a wide range of objects, as quickly and efficiently as well as easily as possible.
The most widely used models in the Geometric Modeling Systems are:
Constructive Solid Geometry (CSG) and Boundary Representations (BRep).
However, these have their limitations too. Boolean ...

I have five different papers that I need to have written. Disciplines should be in Mathematical methods in introductory algebra,geometry,business math word problems,and business statistics

1 pages (250 words)

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...Arithmetic and Geometric Sequences Submitted Introduction: The arithmetic and geometric sequence aretwo of the simplest sequences in mathematics. In arithmetic sequence, each successive term is derived by adding (or subtracting) a constant number. For example: 1, 4, 7, 10 and so on. In geometric sequence, each successive term is obtained by multiplying (or dividing) the previous term by a constant. For example: 2, 6, 18, 54 and so on.
Exercise 35
A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of the labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the next 10 feet will cost... and...

Impacts of Johann Carl Friedrich Gauss as a Mathematician

4 pages (1000 words)

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...Geometry Today, Johann Carl Friedrich Gauss is widely considered as the prince of mathematics. Surprisingly though, Gauss is barely known to the present-day students of mathematics either as a geometer or as a genius. Yet, Gauss, or his mathematical ideas/theories, had created a stir in the world of mathematics, both past and present. For one, Gauss had proposed a revolutionary idea about the universe in general and the spatial dimension in particular. By and large, this exception mathematician -- a German by nationality and a mathematician by profession -- had made a great impact to the realm of mathematics. In his lifetime, Gauss had... ?The Impact of Johann Carl Friedrich Gauss’s Anti-Euclidean...

Math Project

2 pages (500 words)

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...geometry has been explained in depth. Apparently, geometry is something that everyone uses daily. It is found everywhere:space,sports,machines,art,cars and so much more. A major contributor in the geometry world who goes by the name Euclid(350BC),enlighten us on what geometry is all about. Through Euclidean geometry, we are able to answer some of the questions like why or where symbols such as Pi( π) or the Pythagorean theorem was derived from. However, this paper will answer will answer some of the interesting question evolving around Euclidean geometry.
Project Questions
1. The number pi(π)has an interesting history... Mathematical Project Due Introduction In this research paper, the symbol pi(π) in...

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