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...Dr. Muhammad Maqbool MAT 121, Research Project 2 January 29, 2008 Fractal Geometry A fractal is generally “a rough or fragmented geometric shape that can be subdivided into parts.” One of the ways that fractal geometry is used is in the area of medicine. In the past few years fractal analysis techniques have gained increasing attention in signal and image processing, especially in medical sciences such as Pathology. Fractal analysis has found applications in the detection of coding regions in DNA and measurement of the space-filling properties of tumors, blood vessels and neurons. Fractal concepts have also been usefully incorporated into models of biological processes, including cell growth, blood vessel growth, periodontal disease and viral infections. Other very interesting applications are founded in medical imaging Fractal analysis is widely used in image processing, both in characterizing shapes of objects and in assessing texture. Breast masses present shape and texture characteristics that vary between benign masses and malignant tumors in mammograms. Limited studies have been conducted on the application of fractal analysis specifically for classifying breast masses. The fractal dimension of the contour of a mass may be computed either directly from the two dimensional contour or from one-dimensional signatures derived from the contour. Other ways that fractal geometry is use is in biology with different applications and techniques use to classify and...

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...UNIVERSITY OF SCIENCE AND TECHNOLOGY Lapasan, Cagayan De Oro City COLLEGE OF ENGINEERING & ARCHITECTURE B.S. in Architecture Major in Architecture BSARCH SY 2007-2008 SUBJECT CODE DESCRIPTIVE TITLE LAB LEC H O U R LAB U LEC CREDIT N I T PRE-REQUISITE CO-REQUISITE 1ST YEAR -1ST SEMESTER ARCH10 Architectural Design 1 (Introduction to Design) 1.0 3.0 1.0 1.0 2.0 ARCH20 Graphics 1 (Mechanical Drawing) 1.0 6.0 2.0 1.0 3.0 ARCH30 Visual Tech 1 (Monochromatic & Freehand 0.0 6.0 2.0 0.0 2.0 Drawing) ARCH50 Theory of Architecture 1 3.0 0.0 0.0 3.0 3.0 ENGL11 Study & Thinking Skills 3.0 0.0 0.0 3.0 3.0 PD10 Essence of Personality 1.0 0.0 0.0 1.0 1.0 MATH 17 Algebra & Trigonometry 6.0 0.0 0.0 6.0 6.0 NSTP10 ROTC/CWTS/LTS 1 3.0 0.0 0.0 3.0 3.0 18.0 15.0 5.0 18.0 23.0 1ST YEAR -2ND SEMESTER ARCH11 Architectural Design 2 (Creative Design & 1.0 3.0 1.0 1.0 2.0 ARCH10 Fundamentals) ARCH21 Graphics 2 (Perspective Shades & Shadows) 1.0 6.0 2.0 1.0 3.0 ARCH20 ARCH31 Visual Tech 2 (Color Rendering & Still Life) 0.0 6.0 2.0 0.0 2.0 ARCH30 ARCH40 History of Architecture 1 3.0 0.0 0.0 3.0 3.0 ARCH51 Theory of Architecture 2 3.0 0.0 0.0 3.0 3.0 ARCH50 ENGL20 Writing Across Disciplines 3.0 0.0 0.0 3.0 3.0 ENGL11 PD20 Social Graces & Social Relations 1.0 0.0 0.0 1.0 1.0 PD10 MATH32b Differential Calculus w/ Analytic Geometry 5.0 0.0 0.0 5.0 5.0 MATH 17 NSTP20 ROTC/CWTS/LTS 2 3.0 0.0 0.0 3.0 3.0 NSTP10 20.0 15.0 5.0......

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...Geometry Geometry is all about shapes and their properties. If you like playing with objects, or like drawing, then geometry is for you! Geometry can be divided into: Plane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper Solid Geometry is about three dimensional objects like cubes, prisms and pyramids. Plane Geometry Plane geometry is all about shapes like lines, circles and triangles ... shapes that can be drawn on a flat surface called a Plane (it is like on an endless piece of paper). Plane A plane is a flat surface with no thickness. Our world has three dimensions, but there are only two dimensions on a plane. Examples: • • length and height, or x and y And it goes on forever. Examples It is actually hard to give a real example! When we draw something on a flat piece of paper we are drawing on a plane ... ... except that the paper itself is not a plane, because it has thickness! And it should extend forever, too. So the very top of a perfect piece of paper that goes on forever is the right idea! Also, the top of a table, the floor and a whiteboard are all like a plane. Imagine Imagine you lived in a two-dimensional world. You could travel around, visit friends, but nothing in your world would have height. You could measure distances and angles. You could travel fast or slow. You could go forward, backwards or sideways. You could move in straight lines, circles, or anything so......

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...Geometry Notes First Class Point has zero dimensions Postulates/Axioms: statement we accept as being true without a proof Theorems/Corollaries: statement that must be proven before we accept it as being true Corollaries are spin off of another theorem Postulates * P1-1 Given any two points, there is a unique distance between them * P1-2 any segment has exactly one midpoint Theorem * T1-1 “Midpoint Theorem” If m is the midpoint of segment AB, then: 2AM=AB, AM=1/2AB and 2MB=AB, MB=1/2 AB Vocab: Collinear: points that are on the same straight line Noncollinear Points: Points that are not on same straight line Obliquely intercept: not at 90 degree angle Three positions for two lines in space 1. Skew lines: never intercept and not parallel. 2. Parallel Lines: never intercept 3. Intercepting lines: cross each other Planes Planes go on forever, never end, like lines. Line can be: * in plane * Intercept plan * Parallel with plane Two relationships for Planes 1) Parallel 2) Intercept Space contains all points Line with 4 colinear points Can name it line L, or take two points on the line and same it that way. AB, AC, AD, BC, BD, with arrows on top. Subsets of line. * Rays, has only one arrow on top cause starts at point, * Rays going in diff direction on line called opposite rays, same starting points, but opposite directions * Can’t change lettering around with rays cause first letter is...

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...Islamic Impact on City/Town Planning Course : Muslim Heritage and its Global Impact (Spring 2013) sec. 02 Date : 3/19/2013 Table of contents 1. INTRODUCTION 2. THE CITY 2.1. PRE-ISLAMIC PRECEDENTS 2.2. FORMATION OF URBAN MODELS 3. DESIGN PRINCIPLES OF THE ISLAMIC CITY 3.1. NATURAL LAWS 3.2. RELIGIOUS AND CULTURAL BELIEFS 3.3. DESIGN PRINCIPLES STEMMED FROM SHARIAH LAW 3.4. SOCIAL PRINCIPLES 4. MORPHOLOGICAL COMPONENTS OF THE ISLAMIC CITY 4.1. THE MAIN MOSQUE 4.2. SUQS 4.3. RESIDENTIAL QUARTERS -COURTYARDS 4.4. STREET NETWORK 4.5. WALL 4.6. EXTERIOR 4.7. ELEMENTS ABOVE THE STREET. 4.8. ISLAMIC EXTERIOR AND INTERIOR DECORATION 4.9. THE WAQF 4.10. WATER SYSTEMS 4.11. SERIAL AND CONTINUOUS SHAPES OF WATER 4.12. POLAR AND CLOSED WATER SHAPES 5. CONCLUSION 6. REFERENCES 3 4 4 4 6 7 7 7 7 8 9 9 11 12 12 12 12 12 13 14 15 18 19 20 |Page2 1. Introduction Man is a natural planner and all through history has planned for his own changing needs and for the needs of those around him. His towns and cities have been subject to continual 'progress' and 'modernization', evolving, adapting and assimilating new ideas and technologies. The changes came about through additions, alterations and adjustments to what was there before and in a way that continued to allow each place its own expression of culture and society. The infinite variety and diversity of mankind is identified by cultural preferences, modes of social behavior and interaction, rationale, intellect, beliefs,......

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... conventional banks and Islamic banks. In simple words Islamic banks operate in interest free system. Prohibition of interest is ordained in Islam in all forms and intent. This Prohibition is strict, absolute and unambiguous. The Holy Qur'an in verse 278 of Surah Al-Baqarah states: "O ye who believe! Fear Allah and give up what remains of your demand for Riba, if ye are indeed believers." Verse 2: 279 says: "If you do it not, take notice of war from Allah and His Messenger. But if ye turn back, ye shall have your capital sums. Deal not unjustly and you shall not be dealt with unjustly." It therefore, follows that interest is prohibited as it leads to injustices and Islam is against all forms of injustices and exploitations and pleads an economic system, which aims at securing extensive socio-economic justice. The Islamic law of prohibition of Riba, which includes interest, was originally not based on economic theory but on Divine Authority, which considers the charging of interest as an act of injustice (Dr. Siddiqui). Islamic banks appeared on the world scene as active players two decades ago. But many of the principles on which Islamic banking is based have been commonly acceptable all over the world for centuries rather than decades, as it is evident that Islamic finance was practiced predominantly in the Muslim world throughout the middle Ages, promoting trade and business activities. In Spain and the Mediterranean and Baltic States, Islamic merchants became......

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...developing mathematical arguments about geometric relationships. According to "Geometry Standard" (2013),”They will be able to recognize, and name two dimensional shapes, as well as describing the attributes as well as the parts of two and three dimensional shapes.” They also will be able to show the locations as well as the spatial relationships by using coordinate geometry and other representational systems. According to "Geometry Standard" (2013)”They will be able to show, name and interpret relative positions in space, and apply ideas about relative position.” They are definitely going to be able to apply the different transformations and they will also be able to use symmetry to discover mathematical situations.” “They will be able to recognize and know the different sides, flips as well as the turns. ("Geometry Standard", 2013). Lastly they be able to use visualization, and modeling to solve problems. “They will be able to recognize geometric shapes in their environment and can show their location.” ("Geometry Standard", 2013). With this activity and game I believe that my students will learn geometric shapes in a fun and exciting way, because they will not realize they are learning, but they will think that they are having fun. I also believe that students with learning problems can benefit as well, because they will be in small groups, and will be able to feed off each other. Geometry Standard. (2013). Retrieved from......

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...History of Geometry Geometry was thoroughly organized in about 300 BC, when the Greek mathematician Euclid gathered what was known at the time, added original work of his own, and arranged 465 propositions into 13 books, called 'Elements'. The books covered not only plane and solid geometry but also much of what is now known as algebra, trigonometry, and advanced arithmetic. Through the ages, the propositions have been rearranged, and many of the proofs are different, but the basic idea presented in the 'Elements' has not changed. In the work facts are not just cataloged but are developed in a fashionable way. Even in 300 BC, geometry was recognized to be not just for mathematicians. Anyone can benefit from the basic learning of geometry, which is how to follow lines of reasoning, how to say precisely what is intended, and especially how to prove basic concepts by following these lines of reasoning. Taking a course in geometry is beneficial for all students, who will find that learning to reason and prove convincingly is necessary for every profession. It is true that not everyone must prove things, but everyone is exposed to proof. Politicians, advertisers, and many other people try to offer convincing arguments. Anyone who cannot tell a good proof from a bad one may easily be persuaded in the wrong direction. Geometry provides a simplified universe, where points and lines obey believable rules and where conclusions are easily verified. By first studying how to reason......

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...Assignment: Report on Islamic architecture (Wazir Khan Mosque) 1. Introduction A distinctive example of Islamic architecture can be seen in Wazir Khan Mosque. It is the most exquisite mosque in the Mughal era. This building is famous because of its magnificent designs and decorations. Also, its great history played a role in placing it as one of the most beautiful and honorable Islamic buildings in the world. 2. Background 3.1 Location Wazir Khan Mosque is located in Lahore district in Punjab province in Pakistan beside Delhi Gate from the east and Lahore Fort from the west (Wazir Khan Mosque, 2011). Actually, it is accessed after passing a bustling bazaar in Rang Mahal Road, then an imoposing mosque appears beyond it. (Omar, 2008). 3.2 Type of Building Wazir Khan Mosque or Masjid Wazir Khan is an Islamic mosque that was built for praying purposes as other mosques. 3.3 Purpose of Building The mosque was built for commercial and religious purposes (Wazir Khan Mosque). It is used as a place for Islamic worship such as praying, and for gaining profits from the bath house which is called (shahi Hammam) and from the markets around the mosque. The income was employed in maintenance projects for the mosque to ensure that it will still forever (Wazir Khan Mosque, 2011). Indeed, the mosque was built on the existing grave of Sayed Muhammad Ishaq who was known as Miran Badshah. Also, it was used as a place of studying especially with the rooms...

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...Victorian Architecture from 123.com During the Victorian period, there was a revival of classical (Greek and Roman), Gothic, Renaissance and Baroque architecture. Romantic architects replicated Greek and Roman buildings, which were revered as the ultimate examples of beauty (Sporre 487; Tansey 932). Increased nationalism in England also sparked a revival of Gothic architecture. After the Houses of Parliament burnt down in London (1834), the task of redesign the new building was assigned to Charles A. Barry and Augustus W. N. Pugin. Their Gothic design of the new Houses of Parliament make it a prime example of Victorian architecture today (Tansey 955). It is important to recognize that Romantic architecture was not only a return to the past. Modern technologies and materials, as well as non-European influences, also played a role. (Sporre 495-98; Tansey 956). One example is the Crystal Palace designed by Sir Joseph Paxton for the Great Exhibition in London (1851). Made of iron and glass, it was designed to be rapidly put together and taken apart. Another noted architectural example of this period was John Nash’s Royal Pavilion in Brighton (1815-18). The design of this palace was greatly influenced by Islamic and Eastern architecture (Flynn; Sporre 495-98; Tansey 956, 1014). Victorian architecture was both a rediscovery of the past and the precursor of Modern architecture. Some buildings embodied both of these characteristics. The Houses of Parliament and the Crystal...

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...New York State Common Core Mathematics Curriculum GEOMETRY • MODULE 1 Table of Contents1 Congruence, Proof, and Constructions Module Overview .................................................................................................................................................. 3 Topic A: Basic Constructions (G-CO.1, G-CO.12, G-CO.13).................................................................................... 7 Lesson 1: Construct an Equilateral Triangle ............................................................................................. 8 Lesson 2: Construct an Equilateral Triangle II ........................................................................................ 16 Lesson 3: Copy and Bisect an Angle........................................................................................................ 21 Lesson 4: Construct a Perpendicular Bisector ........................................................................................ 30 Lesson 5: Points of Concurrencies .......................................................................................................... 37 Topic B: Unknown Angles (G-CO.9) ..................................................................................................................... 43 Lesson 6: Solve for Unknown Angles—Angles and Lines at a Point ....................................................... 44 Lesson 7: Solve for Unknown Angles—Transversals .................................

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...Geometry Manipulative Handout Joan L. Holyfield Math/157 March 8, 2015 Instructor: James Paga Geometry Manipulative Handout The geometry manipulative that I chose to present is how to make a Geo City. With making a Geo City, it teaches students in grades 3-5. This math exercise encompasses learning and identifying cubes, pyramids, cones, rectangular and other shapes in different sizes which are appropriate for this age group. This activity can be done in a group setting, with each child having a share in identifying different geometrical shapes, and putting them in a real-world setting. By using these different geometric shapes to construct buildings and cars, the children will learn about spatial visualization, location and coordinate points, and transformation. The Geo City will help to reinforce the relationships with two and three-dimensional shapes that have already been learned in previous classes. The students will also be able to explore the effects of rotating, reflecting, and transforming shapes. The Geo city also lends itself to real world application by simulating a city block that they may find in their neighborhood. Then they can begin to understand how the geometric shapes are a part of their everyday lives. Constructing the Geo City also helps the children with their mapping and graph skills, because they will be using both to first, decide how to design the city (using graph paper or geo dot paper), then by deciding where to put the......

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...Geometry Manipulatives MTH 157 April 6, 2015 Lynn Shevelenko Geometry Manipulatives I used www.geogebra.org and I used it to manipulate the shapes and I used it to create shapes as well. These tools are great, I think I can see being able to use them in the classroom setting I think that this tool will be something that is very helpful for students to learn how to create shapes and how to turn one shape into another. I will use this tool to have them make a shape and then have one of the other students take that shape and turn it into another shape. I would also have them do this in a setting without the tool, I would have one student draw a shape, and then have another student use their pencil to change the shape by using a different color pencil and have it go around the circle to see how many shapes they could make with the one starting shape. With little kids I feel that it is important to have as many interactive activities as possible just because it is a fun way for them to learn, and I think that it would be a good way for them to remember the activity and remember how they did what they did with the coloring in groups. Group activities are also a fun way for kids to learn. It is another interactive way for students to learn as well as get some energy out of their systems so that way recess is not the only time the get to run around and get their energy out. I think that the www.geogebra.org website is a great way for the kids to have an interactive experience...

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...Islamic Architecture in the UAE Many cities all over the world are developing to become important urban areas in all respects like Tokyo, New York and Mumbai. Every city has some reasons for their develop like building factories, importance of the location and much more. On the other hand there are some cities that had decline like Detroit, Flint and Cleveland because they only have depended on one resource for income. Abu Dhabi has grown through its economic vision and it is trying to sustainable its development through diversification to avoid declining. Development and growth in cities is shown through some reasons. The strategic location of the city. For this reason, most major cities are on rivers or at the junction of important overland routes (City, 2008). Moreover some cities owe for the importance of religion and became centers of worship (City, 2008). For example the city of Rome survived the collapse of the Roman empire because it was the capital of western Christendom (City, 2008). Early cities that developed strong military forces added to their territory, wealth and importance by conquest. Favorably located settlements often became large and prosperous through commerce (City, 2008). Also some modern cities owe to their development and to the fact that they were built as national capitals. Like Washington, D.C; Canberra, Australia (City, 2008). Climate also is a an important factor; the cities of Florida owe much of their growth to the state’s...

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...The word geometry is Greek for geos - meaning earth andmetron - meaning measure. Geometry was extremely important to ancient societies and was used for surveying, astronomy, navigation, and building. Geometry, as we know it is actually known as Euclidean geometry which was written well over 2000 years ago in Ancient Greece by Euclid, Pythagoras, Thales, Plato and Aristotle just to mention a few. The most fascinating and accurate geometry text was written by Euclid, and was called Elements. Euclid's text has been used for over 2000 years! Geometry is the study of angles and triangles, perimeter, area and volume. It differs from algebra in that one develops a logical structure where mathematical relationships are proved and applied. In part 1, you will learn about the basic terms associated with Geometry. Terms (Undefined) 1. Point Points show position. A point is shown by one capital letter. In the example below, A, B, and C are all points. Notice that points are on the line. 2. Line A line is infinite and straight. If you look at the picture above, is a line, is also a line and is a line. A line is identified when you name two points on the line and draw a line over the letters. A line is a set of continuous points that extend indefintely in either of its direction. Lines are also named with lowercase letters or a single loswer case letter. For instance, I could name one of the lines above simply by indicating an e. Terms (Defined) 1. Line Segment A......

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