Alexander Zouev 000051 - 060 - 3 - Extended Essay – Mathematics Alhazen’s Billiard Problem Introduction: Regarded as one of the classic problems from two dimensional geometry‚ Alhazen’s Billiard Problem has a truly rich history. The problem is believed to have been first introduced by Greek astronomer Ptolemy back in 150 AD1 and then eventually noticed by 17th century Arabic mathematician Abu Ali al Hassan ibn Alhaitham (whose name was later Latinized into Alhazen)2 . Alhazen
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WT + 15 = 20 WT = 5 6-6 Trapezoids and Kites Find each measure. 1. ANSWER: 5 COORDINATE GEOMETRY Quadrilateral ABCD has vertices A (–4‚ –1)‚ B(–2‚ 3)‚ C(3‚ 3)‚ and D(5‚ –1). 3. Verify that ABCD is a trapezoid. SOLUTION: First graph the points on a coordinate grid and draw the trapezoid. SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So‚ each pair of base angles is congruent. Therefore‚ ANSWER: 101 2. WT‚ if ZX = 20 and TY = 15 SOLUTION: The trapezoid WXYZ is an isosceles trapezoid
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Kuta Software - Infinite Geometry Name___________________________________ Arcs and Central Angles Date________________ Period____ Name the arc made by the given angle. 2) ∠1 1) ∠FQE I F H 1 Q J E D Name the central angle of the given arc. 3) ML 4) ML L L M K 1 Q M K If an angle is given‚ name the arc it makes. If an arc is given‚ name its central angle. 6) Major arc for ∠1 5) RS B T C Q 2 1 3 S R A 7) ∠KQL
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MATHEMATICS CURRICULUM FOR SECONDARY COURSE RATIONALE Mathematics is an important discipline of learning at the secondary stage. It helps the learners in acquiring decision- making ability through its applications to real life both in familiar and unfamiliar situations. It predominately contributes to the development of precision‚ rational and analytical thinking‚ reasoning and scientific temper. One of the basic aims of teaching Mathematics at the Secondary stage is to inculcate the skill
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the future? These are a few of the many questions that one asks when they have to take an algebra course. This is a required subject in most colleges to further ones education. The first year of algebra is a prerequisite for all higher-level math: geometry‚ algebra II‚ trigonometry‚ and calculus. It is quite true‚ while many people get by without an education in algebra‚ whenever they pick up the phone‚ manage their money‚ travel to some other place‚ they are unintentionally using math. Algebraic
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ABC’S OF GEOMETRY | By Parker Davis | January 2‚ 2012 | AA similarity | when two triangles have corresponding angles that are congruent as shown below‚ the triangles are similar | | AAS | if two angles and the non-included side one triangle are congruent to two angles and the non-included angle of another triangle‚ then these two triangles are congruent | | Acute angle | an angle with an angle measure less than 90° | | Acute triangle | a triangle where all three internal angles are acute
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FORM 5 MATHEMATICS Chapter 3 TRANSFOMATION 111 NAME :__________________________________________ FORM 5 _________________________ 3.1 TRANSLATION (a) Base on the graph below‚ state the translation (i) A → A’ translation (ii) B → B’ (iii) C → C’ (iv) D → D’ (v) E → E’ (b) A Point P is located at coordinates (4‚3) on a Cartesian plane. P’ is the image of P under a translation
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Solids Content Area: Math Grade Level: Kindergarten Time Frame: 45 min Prior to this lesson the students had a lesson on attributes. The children defined and identified attributes in different two-dimensional shapes. MA Framework Standard: Geometry K.G Identify and describe shapes (squares‚ circles‚ triangles‚ rectangles‚ hexagons‚ cubes‚ cones‚ cylinders‚ and spheres). 2. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying
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Math in My Life This year in Algebra 2 class I have learn some very interesting and important topics. Throughout this past school year I have grown and learned how to use these newly learned skills and my understanding of algebra is now complete. In math class this year‚ I believe I did fairly well and received almost got all A’s. I think I passed this class is because math in general comes easy to me. I only studied in the beginning of the year‚ as the latter part of the year came much easier.
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The work of Maurits Carnelis Escher (M.C. Escher) is widely considered the most popular example of the mathematical influence in art. Though never formally trained in math‚ Escher’s initial interest in decorative art sparked a curiosity in certain mathematical areas such as geometric shapes‚ tessellations and spatial planes/demensions. His interest in both aesthetic and logic resulted in provoking visual representations of multiple dimension. Escher’s understanding of mathematics in combination
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