Rotations and Translations
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1 Rotations and Translations Lecture 33 Sections Robb T. Koether Hampden-Sydney College Wed, Nov 20, 2013 Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
2 1 Symmetry in Faces 2 Rotation of Faces 3 Rotations 4 Assignment Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
3 Outline 1 Symmetry in Faces 2 Rotation of Faces 3 Rotations 4 Assignment Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
4 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
5 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
6 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
7 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
8 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
9 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
10 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
11 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
12 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
13 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
14 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
15 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
16 Symmetry in Faces Who is this? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
17 Outline 1 Symmetry in Faces 2 Rotation of Faces 3 Rotations 4 Assignment Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
18 Rotation of Faces A happy grandmother Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
19 Rotation of Faces An upside-down happy grandmother Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
20 Rotation of Faces An upside-down happy grandmother Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
21 Rotation of Faces An unhappy grandmother? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
22 Rotation of Faces A happy girl Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
23 Rotation of Faces An upside-down happy girl Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
24 Rotation of Faces An upside-down happy girl Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
25 Rotation of Faces An unhappy girl? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
26 Outline 1 Symmetry in Faces 2 Rotation of Faces 3 Rotations 4 Assignment Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
27 Rotations Definition (Rotation) A rotation is rigid motion that rotates an object about a fixed point called the center of rotation. The angle is called the angle of rotation. Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
28 Examples The object is rotated 90 clockwise about the center (black dot). Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
29 Examples The object is rotated 180 clockwise about the center (black dot). Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
30 Examples Locating the Center of Rotation Two points on a circle Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
31 Examples Locating the Center of Rotation Connect them with a chord Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
32 Examples Locating the Center of Rotation Find the midpoint of the chord Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
33 Examples Locating the Center of Rotation The perpendicular bisector passes through the center of the circle Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
34 Examples The object and its image Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
35 Examples A' A Select a point A and its image A Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
36 Examples A' A Draw the segment AA Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
37 Examples A' A Draw the perpendicular bisector of AA Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
38 Examples B A' B' A Select another point B and its image B Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
39 Examples B A' B' A Draw the segment BB Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
40 Examples B A' B' A Draw the perpendicular bisector of BB Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
41 Examples B O A' B' A The intersection of the bisectors is the center of rotation Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
42 Characteristics of Rotations Characteristics of Rotations A rotation has exactly one fixed point, its center of rotation. A rotation is determined by two points and their images. A 360 (or a 0 ) rotation is the identity motion. Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
43 Sequences of Rotations Sequences of Rotations A reflection followed by a reflection is a rotation! Is a rotation followed by a rotation again a rotation? Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
44 Outline 1 Symmetry in Faces 2 Rotation of Faces 3 Rotations 4 Assignment Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
45 Assignment Assignment Page 347: Exercises 13, 17, 20, 23, 26, 28. Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, / 35
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