SOLUTION MANUAL For A SURVEY OF CLASSICAL AND MODERN GEOMETRIES With Computer Activities 1st Edition By Arthur Baragar

SOLUTION MANUAL For A SURVEY OF CLASSICAL AND MODERN GEOMETRIES With Computer Activities 1st Edition By Arthur Baragar-Exercise 1.1. Suppose that at the spring solstice the angle between a star, the Earth, and the sun measures 79.1 ◦, and at the fall solstice the angle measures 100.8 ◦. How far away is the star from the Earth? (The Earth is 93 million miles from the sun.) The solution is in the text. Exercise 1.2. The numbers in Exercise 1.1 were cooked up. From your general knowledge, are these numbers reasonable? Explain. Solution. In Exercise 1.1, we found that the star is 100,000,000,000 miles away. Let us convert this figure to light years. A light year is how far light travels in a year. Since light travels at a speed of 186,000 miles per second, one light year is the same as 1 lightyear = 186, 000 miles yr 3600 sec 24 hrs 365 day sec hr day yr = 5.87 × 1012 miles. Thus, the distance to the star in Exercise 1.1 is 1011 miles 1 lightyear 5.87 × 1012 miles = .017 lightyear. Since this is much smaller than 4.3 lightyears, the distance to the nearest star (other than the Sun), we conclude that the numbers are not reasonable. Exercise 1.3. What order of magnitude is the difference between 180◦ and the sum of the angles for the summer and winter observations of Alpha Centauri? (See Figure 1.1.) 1 2 CHAPTER 1. EUCLIDEAN GEOMETRY 15hrs 14hrs 13hrs 12hrs Figure 1.1. The nearest star (other than the sun) is Alpha Centauri, also known as Rigil Kentaurus, which is 4.3 light years away. This star is the α or brightest star in the Centaurus constellation, which is just south of Libra. It is visible from June to December in the nighttime sky of the southern hemisphere. It briefly appears above the southern horizon in parts of Florida and southern Texas.