Tonne

The tonne (ⁱ/tʌn/) (British and SI; SI symbol: t) or metric ton (in the United States) is a non-SI metric unit of mass equal to 1,000 kilograms; or one megagram (Mg); it is equivalent to approximately 2,204.6 pounds,1.10 short tons (US) or 0.984 long tons (imperial). Although not part of the SI per se, the tonne is "accepted for use with" SI units and prefixes by the International Committee for Weights and Measures, along with several other units like the bar, litre and day.

Symbol and abbreviations

The SI symbol for the tonne is "t", adopted at the same time as the unit itself in 1879. Its use is also official within the United States, having been adopted by the US National Institute of Standards and Technology. It is a symbol, not an abbreviation, and should not be followed by a period. Informal and non-approved symbols or abbreviations include "T", "mT", "MT", and "mt". Some of these are actually SI symbols for other units: "T" is the SI symbol for the tesla and "Mt" is the SI symbol for megatonne (equivalent to one teragram); if describing TNT equivalent units of energy, this is equivalent to 4.184 petajoules.

Megagon

A megagon is a polygon with 1 million sides (mega-, from the Greek μέγας megas, meaning "great"). Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle.

Regular megagon

A regular megagon is represented by Schläfli symbol {1000000} and can be constructed as a truncated 500000-gon, t{500000}, a twice-truncated 250000-gon, tt{250000}, a thrice-truncated 125000-gon, ttt{125000), or a four-fold-truncated 62500-gon, tttt{62500}, a five-fold-truncated 31250-gon, ttttt{31250}, or a six-fold-truncated 15625-gon, tttttt{15625}.

A regular megagon has an interior angle of 179.99964°. The area of a regular megagon with sides of length a is given by

The perimeter of a regular megagon inscribed in the unit circle is:

which is very close to 2π. In fact, for a circle the size of the Earth's equator, with a circumference of 40,075 kilometres, one edge of a megagon inscribed in such a circle would be about 40 meters long. The difference between the perimeter of the inscribed megagon and the circumference of this circle comes to less than 1/16 millimeters.