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The position problems (sheet) By Dr. Samah Mohamed Mabrouk www.smmabrouk.faculty.zu.edu.eg By Dr. Samah Mohamed Mabrouk www.smmabrouk.faculty.zu.edu.eg
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Problem (3): Represent a rhombus ABCD, its vertex B is given, its side AD a given plane , its vertex C a given str. Line m and the vertex A(?,?,2.1). D A C B m Position prob.Dr. Samah Mohamed Mabrourk
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Given α, A مستوي و نقطة خارجه Req β //α, A є β Given α, A مستوي و نقطة خارجه Req β //α, A є β X 12 vv hh A2A2 A1A1 vv hh V1V1 V2V2 Position prob.Dr. Samah Mohamed Mabrourk
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Given α, A مستوي و نقطة خارجه Req β //α, A є β Given α, A مستوي و نقطة خارجه Req β //α, A є β X 12 vv hh A2A2 A1A1 vv hh H1H1 H2H2 Position prob.Dr. Samah Mohamed Mabrourk
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x 12 vv hh vv hh H1H1 V2V2 V1V1 H2H2 m1m1 m2m2 Position prob.Dr. Samah Mohamed Mabrourk خط تقاطع مستويين. ( المستويين فى حالة عامة )
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x 12 vv hh vv hh H1H1 V2V2 V1V1 H2H2 = m 1 m2m2 Position prob.Dr. Samah Mohamed Mabrourk خط تقاطع مستويين. ( عام و خاص )
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x 12 vv hh H2H2 m2m2 m1m1 H1H1 V2V2 V1V1 R 2 R 1 =h vv Position prob.Dr. Samah Mohamed Mabrourk تقاطع خط مع مستوى.
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x 12 vv hh H2H2 m2m2 m1m1 H1H1 V2V2 V1V1 R 2 R 1 = v Position prob.Dr. Samah Mohamed Mabrourk تقاطع خط مع مستوى. h
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Problem (3): Represent a rhombus ABCD, its vertex B is given, its side AD a given plane , its vertex C a given str. Line m and the vertex A(?,?,2.1). C2 C2 C1 C1 h h v v h h v v m2 m2 m1 m1 B2 B2 B1 B1 x 12 = v h h D A C B m 2.1 L :A 2 L :A 1 V2 V2 V1 V1 H1 H1 H2 H2 Position prob.Dr. Samah Mohamed Mabrourk Steps of solu. 1- Draw a L:A 1,A 2 2- B,// 3- m = C
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C2 C2 C1 C1 h h v v h h v v m2 m2 m1 m1 A2 A2 A1 A1 B2 B2 B1 B1 D1 D1 D2 D2 x 12 2.1 L :A 2 L :A 1 z BC C1 C1 B1 B1 T.L. BC = AB z AB A1 A1 B1 B1 T.L. BC = AB L :A 1 Position prob.Dr. Samah Mohamed Mabrourk Steps of sol. 4- Find A (sol. triangles) 5- complete by //
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B1B1 T.L. of m A1A1 z AB B2B2 T.L. of m A2A2 y AB B3B3 T.L. of m A3A3 x AB Triangles of solution Position prob.Dr. Samah Mohamed Mabrourk
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The plane section of solids Position prob.Dr. Samah Mohamed Mabrourk
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1+1+ 6+6+ 8+8+ 9+9+ 4+4+ 10 + 3+3+ 2+2+ 11 + 4 10 Problem (4): Given a right circular cylinder with circular base 1 and is intersected by a plane . Construct the plane section and develop the cylinder, showing the plane section. 1 2 3 4 5 6 7 8 9 11 10 12 8 9 11 6 5 3 7 1 5+5+ 7+7+ 12 + vv hh 2 الإسطوانة هى المجسم الناتج عن دوران مستطيل حول أحد أضلاعه. الضلع الثابت يسمى محور الإسطوانة ( الدوران ) و المتحرك يسمى راسم Position prob.Dr. Samah Mohamed Mabrourk
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7+7+ 1+1+ 1 2 3 4 5 6 7 8 Problem (4): Given a right circular cylinder with circular base 1 and is intersected by a plane . Construct the plane section and develop the cylinder, showing the plane section. 9 11 10 12 8 9 11 6 5 3 2 7 1 1 2 3 4 5 6 7 8 1 9 10 11 12 1+1+ 2+2+ 3+3+ 4+4+ 5+5+ 6+6+ 7+7+ 8+8+ 9+9+ 10 + 11 + 12 + 1+1+ 2+2+ 8+8+ 3+3+ 4+4+ 5+5+ 6+6+ 9+9+ 10 + 11 + 12 + vv hh Position prob.Dr. Samah Mohamed Mabrourk
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تقاطع اسطوانة مع مستوى مائل ( مبنى في العاصمة الدنماركية، كوبناهجن ) Position prob.Dr. Samah Mohamed Mabrourk
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9+9+,11 + 4+4+ 10 +,6 + 2+2+ Problem (5): Given a cone of revolution with base in 1. Construct the plane section of the cone by a given plane . Hence develop the cone, showing the plane section. 1 2 3 4 5 6 7 8 9 11 10 12 3+3+,5 + 1+1+,7 + 8+8+,12 + vv hh V2V2 S 1 =V 1 T.L S2S2 11 + 9+9+ المخروط هى المجسم الناتج عن دوران مثلث قائم الزاوية حول أحد أضلاع الزاوية القائمة. الضلع الثابت يسمى محور المخروط ( الدوران ) و المتحرك يسمى راسم Position prob.Dr. Samah Mohamed Mabrourk
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9+9+,11 + 4+4+ 10 +,6 + 2+2+ Problem (5): Given a cone of revolution with base in 1. Construct the plane section of the cone by a given plane . Hence develop the cone, showing the plane section. 1 2 3 4 5 6 7 8 9 11 10 12 3+3+,5 + 1+1+,7 + 8+8+,12 + vv hh V2V2 S 1 =V 1 10 T.L S2S2 11 + 9+9+ 1 4 3 2 6 5 9 8 7 10 12 11 1 V0V0 1+1+ 6+6+ 5+5+ 4+4+ 3+3+ 2+2+ 7+7+ 8+8+ 9+9+ 1+1+ 11 + 10 + 12 + Position prob.Dr. Samah Mohamed Mabrourk
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المخروط و الإسطوانة فى الهندسة المعمارية
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الكثبان الرملية العلامات المرورية المعدات و الالات Position prob.Dr. Samah Mohamed Mabrourk
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B3B3 B+2B+2 A+2A+2 C+2C+2 D+2D+2 B+1B+1 D1D1 A+1A+1 C+1C+1 B+3B+3 A+3A+3 C+3C+3 C3C3 D3D3 K3K3 K1K1 B1B1 Problem (6): Construct the plane section of a given tetragonal pyramid ABCDV by a given plane . Construct the development of the pyramid withthe plane section. C1C1 A1A1 D2D2 B2B2 A2A2 C2C2 vv hh V2V2 V1V1 V3V3 A3A3 x 13 K2K2 33 D+3D+3 D+1D+1 Position prob.Dr. Samah Mohamed Mabrourk
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B3B3 B+2B+2 A+2A+2 C+2C+2 D+2D+2 B+1B+1 D1D1 A+1A+1 C+1C+1 B+3B+3 A+3A+3 C+3C+3 C3C3 D3D3 K3K3 B1B1 C1C1 A1A1 D2D2 B2B2 A2A2 C2C2 vv hh V2V2 V1V1 V3V3 A3A3 x 13 33 D+3D+3 D+1D+1 z AV A1V1A1V1 T.L V B C D A B A C+C+ D+D+ A+A+ B+B+ A+A+ A Position prob.Dr. Samah Mohamed Mabrourk T.L
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