# Differential Geometry: Geometry in Mathematical Physics and by Greene R., Yau S.-T. (eds.)

By Greene R., Yau S.-T. (eds.)

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Extra info for Differential Geometry: Geometry in Mathematical Physics and Related Topics, Part 2

Sample text

1231231231 . . 6366366636 . . Your Turn a. com/extra_examples b. an irrational number between 1 and 2 Lesson 2–1 Real Numbers and Number Lines 51 The number that corresponds to a point on a number line is called the coordinate of the point. On the number line below, 10 is the coordinate of point A. The coordinate of point B is Ϫ4. Point C has coordinate 0 and is called the origin. B C Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 A 1 2 3 4 5 6 7 8 9 10 11 The distance between two points A and B on a number line is found by using the Distance and Ruler Postulates.

Example 3 7. Algebra In the figure below, M is the midpoint of P ෆQ ෆ. Find the value of x. 2x Ϫ 5 xϩ7 P Exercises Practice • • • • • • • Q • • • • • • • • • • • Use the number line to determine whether each statement is true or false. Explain your reasoning. Homework Help For Exercises M 8–10 11–13, 21, 22 See Examples 1 3 15 2 Extra Practice A B C Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 D E Ϫ3 Ϫ2 Ϫ1 8. ෆ DG GJෆ. ෆ is congruent to ෆ DJෆ. 10. ෆ AG ෆ is congruent to ෆ 12. E is the midpoint of B ෆH ෆ. F 0 1 2 G H 3 4 5 6 I J 7 8 9.

Find the perimeter of a rectangle with a length of 17 feet and a width of 8 feet. Lesson 1–6 A Plan for Problem Solving 35 Another important measure is area. The area of a figure is the number of square units needed to cover its surface. Two common units of area are the square centimeter and the square inch. Abbreviations for units of area use the exponent 2. square inch → in2 square centimeter → cm2 The area of the rectangle below can be found by dividing it into 20 unit squares. 4 in. 5 in. The area of a rectangle is also found by multiplying the length and the width.