In the twenty-first century, societies need to make a wide range of measurements, from economic indicators and population trends to the times of sporting events and various standardized tests. Despite all of the varied measurement that is performed, modern societies still focus attention on the same two subjects, time and distance. In this entry, the focus will be on the measurement of distance.

Early Attempts to Measure Distance

Early civilizations used various crude instruments to measure distance, ranging from a simple pace to measuring rods and marked cords. The accuracy that was achieved with such basic devices can be astonishing. For example, the Great Pyramid of Egypt, built about 2400 B.C.E., has four base edges that are each within 0.01 percent of 751 feet in length.

Most societies developed random units of measure that became standardized over time. The Egyptians used the  cubit, which varied in length from 15 inches to 19 inches, depending on the ruling dynasty. To measure longer distances, some societies employed individuals to pace off the distance. In Egypt, these individuals were called “rope stretchers.” They tied a specific length of rope to their two ankles and then paced off the distance so that each and every stride stretched the rope to its full length. The Egyptians used other crude measuring devices, such as marked cords and wooden rods. Each of the four faces of the Great Pyramid is positioned exactly on one of the four points of the compass. A groma was used to establish right angles for such measuring purposes. The groma was a wooden cross that pivoted and had plumb lines hanging from each arm to ensure proper positioning.

Distance measurement remained static for centuries after the Egyptians, with few advancements. About 500  B.C.E., Greek mathematician Thales demonstrated how to use the geometric principles of similarity to measure distances indirectly. For example, Thales used shadows to measure the height of the Great Pyramid. Still, the data needed for such indirect measurements had to be found using cords and measuring rods.

 Two hundred years later, Greek mathematician Eratosthenes determined the circumference of Earth to within a few hundred miles by using geometric principles and data from rope stretchers. About 200 B.C.E., the astrolabe was invented to measure the angle of elevation of various stars. These data were used to find the time of day, which in turn was used by sailors for navigation. Later developments led to its replacement by the  sextant. In the 1600s, the theodolite was invented, which is a device that measures angles of elevation and horizontal angles simultaneously. The theodolite is essentially a telescope that pivots around horizontal and vertical axes. Modern theodolites can measure angles to an accuracy of 1/3600 of a degree.

In 1620, Edmund Gunther (1581–1626) invented a chain to survey land.

It was 66 feet long and not subject to humidity, fraying, or other irregularities that might affect a rope or cord. The chain was the precursor to the modern steel tape measure. At about the same time, the telescope was invented. This made it possible to see great distances across the heavens and to see stars that had previously been beyond human sight. The distances between celestial bodies remained unknown, but advances in telescopes gave rise to the ability to measure distances across the heavens. During the same time period, Anthony Leeuwenhoek invented the first modern microscope,  opening up a new world of discovery at the opposite end of the measurement spectrum.

Modern Advances in Distance Measurement

The early twentieth century saw great advancements in distance measurements. First, aerial photography made accurate measurements of distances across difficult terrain easily possible. This was followed by satellite photography, making it feasible to survey great tracts of land easily. In the twenty-first century, modern theodolites employ electromagnetic distance measurement processes. These instruments measure the time a laser or ultra high radiation (either microwave for longer distances or infrared radiation for shorter distances) needs to pass over a specific distance. Modern surveying instruments send out a laser pulse to a target on location. The target reflects the laser beam back to the surveyor. The time required to travel out and back is measured by a computer, which then calculates the distance. At the other end of measurable distances, powerful electronic microscopes enable scientists to see increasingly smaller objects.

Modern precision instruments have even affected standard measurement units like the meter. Originally the standard meter was a length of platinum that was exactly one meter long. However, a metallic object can grow or shrink according to atmospheric conditions. The effects of dust and handling can also affect such an object, although only at a microscopic level.

To avoid such effects, a meter is now defined as the distance that light in a vacuum travels in 1/229,792,458 of a second.

Modern precision has made it possible to measure extremely large and small distances. The longest distance measurement is for galaxies that are 14 billion light years from Earth. (Light travels approximately 186,000 miles per second. A light year is how far light travels in a year.) This distance is referred to as 10²⁵ meters. At the other end of the scale, scientists use scanning electron microscopes to see molecular particles that are 10^-16meters long, or 0.1 Fermi in length. (One Fermi is 10^-15 meter.) How much more precision is still possible to achieve is difficult to predict. Most scientists agree that there are objects in the universe that are even farther away from Earth.

Newer, more powerful telescopes will likely be able to detect them and measure their distance from Earth. Scientists also envision a time when objects as small as an individual atom or even subatomic particles will be “visible” and thus can be measured.

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Reference

Dilke, O. A. W. Reading the Past: Mathematics and Measurement. London U.K.: British  Museum Press, 1987.

Morrison, Philip, and Phylis Morrison. Powers of Ten. New York: Scientific American Books, Inc., 1982.

Strauss, Stephen. The Sizesaurus: from Hectares to Decibels, a Witty Compendium of Measurements. New York: Kondasha America, Inc., 1995. 

مواضيع ذات صلة

Dimensions

Dimensional Relationships

Conic Sections

Congruency, Equality, and Similarity

Circles, Measurement of

وتر Chord

هندسة ناقصية Elliptic Geometry

هندسة لا اقليدية Non – Euclidean Geometry

هندسة فضائية Space Geometry

هندسة زائدية Hyperbolic Geometry

هندسة زائدية Hyperbolic Geometry

هندسة تحليلية Analytic Geometry