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Angles megaConverter #17

Introduction and Overview
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Units of common measurement vary widely, from time to time, and place to place. Most units of measurement started as a reference to a physical object or concept. The foot was the length of a man's foot, the inch was the width of a man's thumb, a furlong was the length of a plowed furrow in a field, an acre was the amount of land a man and two oxen could plow in a day, etc. At first, most measurements were only approximations, but eventually many country's governments set each at a specific standard to make commerce possible and fair. Often, when people settled new lands, they used the names of old measurements but set their own standards. Other times, similar sounding measurement names in different countries had greatly different values. Some measurements were derived from other types of measurements, such as a barrel weight being the weight of a barrel of flour. Often, the same measurement had different values depending on the material being measured, such as a wine tun and a beer tun, or a hank of wool and a hank of cotton. These differences made sense to the people that used them, but they seem odd today.

A Frenchman first defined what he called the 'meter' as one ten millionth of the distance from the North Pole to the equator along the Prime Meridian. It was later defined, in a more precise method, as so many wavelengths of a certain color of light. A liter was originally defined as a cubic decimeter, and a kilogram was defined as a liter of pure water at a specified temperature. Later, the standard was changed such that a kilogram mass became the standard and the liter was derived as the volume of a kilogram of water. This has caused the liter to become slightly more than a cubic decimeter.

The International System (SI) was first proposed in France in the 17th century, but was not adopted by France until 1795. The system defined that there was only one standard in each measurement type and each unit greater or less was a power of ten. This made conversions between units much simpler. During the 19th century, several countries made this system their standard, but notably not Britain or the US. In 1965 Britain began changing to the metric system as a condition of membership in the European Common Market. The US government, recognizing the problems of international trade, officially made the metric system its standard in 1975.

Still today, units of common measurements (non-metric) are used throughout the world. It would be hard to forget the foot, yard, mile, quart, gallon, or acre because so many physical objects were based on them. And for convenience sake, it will always be easier to say "a cup" than "two deciliters." It is easier to envision a mile than a kilometer because fence rows, city blocks, and farmland measurements were originally based on the mile.

* Much of our written history still refers to things in common units. The Bible does not refer to meters or kilograms, but to cubits and stadia, or shekels and drachma. Wouldn't it be nice to know what they were talking about way back then? Now you can use megaConverter! For a more complete listing of ancient, foreign, and obsolete measures, download our 'megaSpreadsheet' of conversions in MS Excel format.

Glossary of Conversions:

When two straight lines meet, we say the relative position of the two lines to one another can be expressed as the angle between them. If we hold one line fixed and rotate the other about the meeting point, or vertex, the moving line can rotate through a full circle until it is back at its original position. At one point in the rotation the moving line and the fixed line will be co-incident, one on top the other. This point of co-incidence is defined as the zero point. Now imagine a circle centered on the vertex of the two lines. The line segments of both lines from the vertex to the circle can represent the radius of the circle. Ancient mathematicians determined that the circumference of a circle could be determined by multiplying the diameter of the circle by a constant that we now call pi. This constant is an irrational number, meaning that it cannot be represented exactly by any integer divided by any other integer. Pi is approximately 3.1416. This is close enough for most uses. Mathematicians say that a full circle is represented by an angle of 2*pi radians. If you think about it, this means that a radian is the same angle you would have if you took a circle’s radius and bent it around the circumference of the circle.

There is one other angle measure used, but only rarely, which is gradient measure. The full circle is divided into 400 equal units. This is handy only because the right angle (90 degrees) is now 100 gradients. Each individual gradient can be considered 1 percent of a right angle. This made calculations of things like cannon shell trajectories slightly easier, although with modern electronic computers, this is no longer necessary.

Radian measure is very important for making calculations in geometry, trigonometry, and calculus, but is rather burdensome to use simply describing angles. Ancient Sumerians devised a number system based on 60. They divided the circle into 360 equal parts to describe the angles of lines. This is useful because 360 is divisible by many factors. We call each unit part a degree. A full circle has 360 degrees. If we pass 0 during our rotation around the circle we keep going. Thus, 400 degrees is the same as 400-360=40 degrees. In this way, we can speak not only of angles but of rotations. 720 degrees is 2 full circles. Degrees were also broken down into smaller units of minutes and seconds, where a degree was 60 minutes, and a minute was 60 seconds.

Compasses use points which are 1/32 of a circle or 11.25 degrees.

Note: Because of round-off errors, converting from very large units to very small units or vice-versa may not be accurate (or practical). Conversion factors can be found by converting a quantity of 1 unit to another unit several steps above or below the first. You may need to string several conversion factors together to find the factor from a very large unit to a very small unit, and then you can use a calculator with sufficient digits to find your answer.

Military artillery trajectory calculations sometimes use mils which are 1/6400th of a circle.