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Great Circles and Small Circles

Test your knowledge on Great Circles and Small Circles, which are fundamental concepts in mathematical geography.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is a great circle?

  1. A circle on the Earth's surface that divides the Earth into two equal halves.
  2. A circle on the Earth's surface that passes through the Earth's center.
  3. A circle on the Earth's surface that is perpendicular to the Earth's axis.
  4. A circle on the Earth's surface that is parallel to the Earth's equator.
Question 2 Multiple Choice (Single Answer)

What is a small circle?

  1. A circle on the Earth's surface that divides the Earth into two unequal halves.
  2. A circle on the Earth's surface that passes through the Earth's center.
  3. A circle on the Earth's surface that is perpendicular to the Earth's axis.
  4. A circle on the Earth's surface that is parallel to the Earth's equator.
Question 3 Multiple Choice (Single Answer)

What is the difference between a great circle and a small circle?

  1. Great circles are larger than small circles.
  2. Great circles pass through the Earth's center, while small circles do not.
  3. Great circles divide the Earth into two equal halves, while small circles divide the Earth into two unequal halves.
  4. All of the above.
Question 4 Multiple Choice (Single Answer)

What are some examples of great circles?

  1. The equator
  2. The prime meridian
  3. The Tropic of Cancer
  4. The Tropic of Capricorn
  5. All of the above
Question 5 Multiple Choice (Single Answer)

What are some examples of small circles?

  1. The parallels of latitude
  2. The meridians of longitude
  3. The Arctic Circle
  4. The Antarctic Circle
  5. All of the above
Question 6 Multiple Choice (Single Answer)

What is the shortest distance between two points on the Earth's surface?

  1. A straight line
  2. A great circle
  3. A small circle
  4. It depends on the location of the two points
Question 7 Multiple Choice (Single Answer)

What is the great circle distance between two points?

  1. The distance along a straight line between the two points
  2. The distance along a great circle between the two points
  3. The distance along a small circle between the two points
  4. It depends on the location of the two points
Question 8 Multiple Choice (Single Answer)

How do you calculate the great circle distance between two points?

  1. Use the Pythagorean theorem
  2. Use the law of cosines
  3. Use the haversine formula
  4. Use the Vincenty formula
Question 9 Multiple Choice (Single Answer)

What is the great circle route between two points?

  1. The shortest distance between the two points
  2. The longest distance between the two points
  3. The most direct route between the two points
  4. The least direct route between the two points
Question 10 Multiple Choice (Single Answer)

What are some of the applications of great circles and small circles?

  1. Navigation
  2. Surveying
  3. Cartography
  4. Astronomy
  5. All of the above
Question 11 Multiple Choice (Single Answer)

What is the equation of a great circle?

  1. $$x^2 + y^2 + z^2 = R^2$$
  2. $$x^2 + y^2 - z^2 = R^2$$
  3. $$x^2 - y^2 + z^2 = R^2$$
  4. $$x^2 - y^2 - z^2 = R^2$$
Question 12 Multiple Choice (Single Answer)

What is the equation of a small circle?

  1. $$x^2 + y^2 + z^2 = r^2$$
  2. $$x^2 + y^2 - z^2 = r^2$$
  3. $$x^2 - y^2 + z^2 = r^2$$
  4. $$x^2 - y^2 - z^2 = r^2$$
Question 13 Multiple Choice (Single Answer)

What is the angle between two great circles?

  1. The angle between the two planes that contain the great circles
  2. The angle between the two lines that intersect the great circles at right angles
  3. The angle between the two lines that are tangent to the great circles at the same point
  4. The angle between the two lines that are parallel to the great circles at the same point
Question 14 Multiple Choice (Single Answer)

What is the angle between a great circle and a small circle?

  1. The angle between the two planes that contain the great circle and the small circle
  2. The angle between the two lines that intersect the great circle and the small circle at right angles
  3. The angle between the two lines that are tangent to the great circle and the small circle at the same point
  4. The angle between the two lines that are parallel to the great circle and the small circle at the same point
Question 15 Multiple Choice (Single Answer)

What is the angle between two small circles?

  1. The angle between the two planes that contain the small circles
  2. The angle between the two lines that intersect the small circles at right angles
  3. The angle between the two lines that are tangent to the small circles at the same point
  4. The angle between the two lines that are parallel to the small circles at the same point
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