000RM.dvi
2.2 Lattice points on a circle 113 Appendix: Number of lattice points inside a circle Given a real numberr, how many lattice poi ...
114 Lattice points Exercise 1.Consider the lattice triangleABCwithA=(0,0),B=(36,15) andC=(16,30). Calculate the lengths of the s ...
2.2 Lattice points on a circle 115 Project: Cross number puzzle Fill in the accompanying square with distinct 2-, 3-, and 4-digi ...
116 Lattice points ...
Chapter 3 Equilateral triangle in a rectangle 1 Equilateral triangle inscribed in a rectangle 2 Construction Exercise ...
118 Equilateral triangle in a rectangle 3.1 Equilateral triangle inscribed in a rectangle .... Given a rectangleABCD, how can we ...
3.2 Construction of equilateral triangle inscribed in a rectangle 119 3.2 Construction of equilateral triangle inscribed in a re ...
120 Equilateral triangle in a rectangle Exercise 1.Show that Area(ABP)+ Area(ADQ)= Area(CPQ). P Q A B D C 2.Ta ke a 9 × 10 recta ...
3.2 Construction of equilateral triangle inscribed in a rectangle 121 5.A piece of 8 × 11 paper is to be cut into a pattern that ...
122 Equilateral triangle in a rectangle ...
Chapter 4 Basic geometric constructions 1 Geometric mean 2 Harmonic mean 3 Equal subdivisions of a segment 4 The Ford circles Ap ...
124 Basic geometric constructions 4.1 Geometric mean .................. We present two ruler-and-compass constructions of the ge ...
4.2 Harmonic mean 125 4.2 Harmonic mean .................. LetABCDbe a trapezoid withAB//CD. If the diagonalsACandBD intersect a ...
126 Basic geometric constructions 4.3 Equal subdivisions of a segment ........... Here is an algorithm to divide a given segment ...
4.4 The Ford circles 127 4.4 The Ford circles .................. The Ford circle of a rational numberr= pqis the circle of radiu ...
128 Basic geometric constructions Appendix: Some basic construction principles Theorem 4.2(Perpendicular bisector locus).Given t ...
4.4 The Ford circles 129 The Geometer’s Sketchpad Basic commands Construct points, segments, lines, circles. Construct a segmen ...
130 Basic geometric constructions Exercise 1.Given triangleABC, construct the equilateral trianglesBCX,CAY andABZexternally on t ...
4.4 The Ford circles 131 6.Two congruent circles of radiiahave their centers on each other. Consider the circle tangent to one o ...
Chapter 5 Greatest common divisor 1 gcd(a, b)as an integer combination ofaandb 2 Nonnegative integer combinations ofaandb 3 Cass ...
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