# There’s a lot more to “Distance” than you think

To put it in simple terms, this frequently talked about word — “distance” — talks about the numerical difference between the location of two places, or how far two objects are. Distance is a widely used term in physics and in various branches of mathematics. Technical though it may appear, but distance is of great importance in the real world as well.

With technological advancements available right in your hands, calculating distance is no more considered as rocket science. All one needs to do is tap on a few icons or punch a few buttons, and flashing on the screens is the answer. However, the technical knowledge of distance, and how to calculate or use it in real life, still holds significance. At times when technology fails, it is only applied knowledge that can save an individual.

One word it may be, but the enormity of distance is far more than can be fathomed. Here are a few things on distance that can help you get a little more acquainted with the vastness of the topic:

Distance and what all can it mean

When referring to the physical distance, it could mean a lot of things, for instance:

The basics — It could be the length of the path, covered between two points, like when navigating a maze.

Orthodromic distance — The shortest distance between two points on a sphere, like the Earth, is known as the orthodromic distance, or the great-circle distance.

Circular distance — It refers to the distance covered by a wheel.

Manhattan distance — The distance that a taxicab might require to cover, north, south, east or west, to reach its destination, on the grid of streets of New York City, is what the Manhattan distance is about.

Chessboard distance — The minimum number of moves that a king in the game of chess might have to make, to travel between two squares, is referred to as chessboard distance.

Euclidean distance — It refers to the straight line between two points in a Euclidean space. Calculated using the distance formula, it is the shortest path possible, through space, when no hurdle is present.

The Pythagorean Theorem and Distance Formula

As mentioned above, the distance formula is one of the methods to calculate distance, or the Euclidean distance, to be specific. As a matter of fact, the distance formula is a condensed form of the Pythagorean Theorem itself.

The Pythagorean Theorem was used to determine the length of a hypotenuse, or the longest side in a right angled triangle, by using the formula H2 (square of the hypotenuse) = P2 + B2, where P and B were the other two sides of the given triangle.

The distance formula, with a little development in the old Pythagorean Theorem, reveals the distance between two points, when their coordinates are known. For instance, let the coordinates of two points A and B be (x1, y1) and (x2, y2). As per the distance formula, d, or the distance, shall be √ [(x2-x1) + (y2-y1)].

The reason behind referring to the latter, or the distance formula, is because it combines all the steps of the Pythagorean Theorem into one, thus saving time and effort.

Author Bio — Emma Thorne is a teacher, blogger, and a mathematics enthusiast. While most people find their peace of mind in family, love, music, or reading, Emma does so in mathematics. She loves sharing knick-knacks and tips and tricks on math with her reader folks, when she isn’t busy educating the tots or writing blogs.

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