Geometry: An Interactive Journey to Mastery

Solution Imagine that the circle is drawn on a tiling of the plane with squares, as shown in Figure 28.2. Here, the rectangle ha ...

Lesson 28: Tilings, Platonic Solids, and Theorems Twelve congruent equilateral triangles are used to construct a tetrahedron an ...

Folding and Conics Lesson 29 Topics x The parabola, ellipse, and hyperbola via folding. x The parabola, ellipse, and hyperbola ...

Lesson 29: Folding and Conics Example 1 3RLQWLQJDÀDVKOLJKWGLUHFWO\WRZDUGDZDOOSURGXFHVDFLUFOHRIOLJKWDJDLQVWWKHZDOO ...

Squaring and simplifying produces the following. 2 22 22 2 2 2 (^1144) 21611216 (^22). xy y xyyyy x yy xy  §·§· ̈ ̧ ̈ ̧©¹©¹  ...

Lesson 29: Folding and Conics D௘ͽ ,VLWSRVVLEOHWRSURGXFHDQRQUHFWDQJXODUSDUDOOHORJUDPDVDFURVV VHFWLRQIURPVRPHSODQD ...

Show that the centers of circles each tangent to a given line and a given circle lie on a parabola. ͼ௘6HHFigure 29.14௘ͽ Figu ...

Lesson 30: The Mathematics of Symmetry The Mathematics of Symmetry Lesson 30 Topics x 0DSSLQJVRIWKHSODQHWUDQVODWLRQVUHÀH ...

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Lesson 30: The Mathematics of Symmetry Solution Assume that the dilation is centered about the origin O and has scale factor k. ...

,GHQWLI\DOOWKHV\PPHWULHVWKDWDQLQ¿QLWHWLOLQJ of equilateral triangles across the entire plane has. ͼ௘6HHFigure 30.4௘ͽ ...

Lesson 31: The Mathematics of Fractals The Mathematics of Fractals Lesson 31 Topics x 7KHGH¿QLWLRQRIDIUDFWDODQGIUDFWDOGL ...

Solution If the area of the entire rectangle is 1 square unit, then the areas of the light-gray regions sum to 11 1 1 3    9 ...

Lesson 31: The Mathematics of Fractals What is the fractal dimension of the fractal in Figure 31.3? 7KH6LHUSLĔVNLVSRQJHLVFR ...

Dido’s Problem Lesson 32 Topics x The legend of Dido. x The isoperimetric problem and its solution. 'H¿QLWLRQ x isoperimetric ...

Lesson 32: Dido’s Problem Because the area of the triangle is^12 × FG × height and FGLVD¿[HGYDOXHWKHWULDQJOHRIPD[LPDOD ...

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Lesson 33: The Geometry of Braids—Curious Applications The Geometry of Braids—Curious Applications Lesson 33 Topics x Braids wi ...

Study Tip x This lesson is purely optional. There are no recommended study tips for this lesson other than to enjoy the lesson ...

Lesson 33: The Geometry of Braids—Curious Applications Show that, with three strands in a braid, a left crossing ͼ௘RIDQ\NLQG௘ ...