Great Circles and Small Circles

Description: Test your knowledge on Great Circles and Small Circles, which are fundamental concepts in mathematical geography.
Number of Questions: 15
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Tags: geography mathematical geography great circles small circles
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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.


Correct Option: A
Explanation:

A great circle is the largest circle that can be drawn on the Earth's surface, and it divides the Earth into two equal halves. Great circles always pass through the Earth's center.

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.


Correct Option: A
Explanation:

A small circle is any circle on the Earth's surface that is not a great circle. Small circles divide the Earth into two unequal halves, and they do not pass through the Earth's center.

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.


Correct Option: D
Explanation:

Great circles are larger than small circles, they pass through the Earth's center, and they divide the Earth into two equal halves. Small circles do not pass through the Earth's center and they divide the Earth into two unequal halves.

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


Correct Option:
Explanation:

The equator, the prime meridian, the Tropic of Cancer, and the Tropic of Capricorn are all examples of great circles.

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


Correct Option:
Explanation:

The parallels of latitude, the meridians of longitude, the Arctic Circle, and the Antarctic Circle are all examples of small circles.

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


Correct Option:
Explanation:

The shortest distance between two points on the Earth's surface is a great circle. This is because a great circle is the largest circle that can be drawn on the Earth's surface, and it always passes through the two points.

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


Correct Option:
Explanation:

The great circle distance between two points is the distance along a great circle between the two points. This is the shortest distance between the two points.

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


Correct Option:
Explanation:

The haversine formula is the most commonly used formula for calculating the great circle distance between two points. It is a relatively simple formula that can be used to calculate the distance between two points on the Earth's surface with a high degree of accuracy.

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


Correct Option:
Explanation:

The great circle route between two points is the shortest distance between the two points. This is because a great circle is the largest circle that can be drawn on the Earth's surface, and it always passes through the two points.

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


Correct Option:
Explanation:

Great circles and small circles have a wide range of applications, including navigation, surveying, cartography, and astronomy. In navigation, great circles are used to calculate the shortest distance between two points on the Earth's surface. In surveying, small circles are used to measure distances and angles. In cartography, great circles and small circles are used to create maps. In astronomy, great circles are used to track the movement of celestial bodies.

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. $$x^2 - y^2 - z^2 = R^2$$


Correct Option: A
Explanation:

The equation of a great circle is $$x^2 + y^2 + z^2 = R^2$$, where R is the radius of the Earth.

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. $$x^2 - y^2 - z^2 = r^2$$


Correct Option: A
Explanation:

The equation of a small circle is $$x^2 + y^2 + z^2 = r^2$$, where r is the radius of the small circle.

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


Correct Option: A
Explanation:

The angle between two great circles is the angle between the two planes that contain the great circles.

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


Correct Option: A
Explanation:

The angle between a great circle and a small circle is the angle between the two planes that contain the great circle and the small circle.

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


Correct Option: A
Explanation:

The angle between two small circles is the angle between the two planes that contain the small circles.

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