Editing 2205: Types of Approximation

In the comic, [[Cueball]], the physicist, generally dealing with theoretical constructs can use straight math, is introducing a problem with the assumption that the particular curve is a (perfectly) circular arc with a radius represented by R. Engineers have to deal with real things, whose dimensions may be known to a certain tolerance. [[Megan]], the engineer, also assumes that the curve is similar to a circle, with a deviation factor of 1/1000.

The joke arises when [[Ponytail]], the cosmologist, uses the much less precise approximation of {{w|pi}} (π) equal to 1. Pi is an irrational number, usually truncated to 3.14. The closest order of magnitude to that is 10 to the 0 power, or 1.

Ponytail offering to use 10 instead of 1 alludes to [//en.wikipedia.org/wiki/Fermi_problem Fermi approximations], as shown in [https://what-if.xkcd.com/84/ Paint the Earth]. Numbers are rounded to the nearest order of magnitude (1, 10, 100, etc.) using a base 10 logarithmic scale. On this scale, "halfway" between 1 and 10 would be &radic;<span style="text-decoration:overline;">10</span> ≈ 3.16. Thus, numbers between about 0.316 and 3.16 are rounded to 1, between 3.16 and 31.6 are rounded to 10, and so on. At about 3.14, pi falls close to this cutoff point, and so by using this form of estimation it doesn't really matter to Ponytail whether pi is approximated to 1 or 10.

Pi is defined as the ratio of the circumference of a circle divided by its diameter. This number is an irrational starting with 3.14 when the geometry is flat. But in curved spaces, the ratios are different. Almost every number can be pi depending on the curvature of the place the circle is residing. The cosmologist doesn't know the curvature of the universe, and so traditional values of Pi may not be more accurate.

This is a parody of the tendency of {{w|cosmology}} to use much rougher approximations in their work. In general, astronomers deal with masses and distances that are so vast that approximations that would be ridiculous elsewhere still yield reasonable answers in astronomy.  

Approximating Pi as 1 may also refer to the habit astronomers have of changing the units of measure such that important constants (such as the speed of light or the gravitational constant) are equal to 1, which highly simplifies the formulas without compromising the math. In this case, the number pi is a dimensionless factor, not a directly measured quantity, which means the math will not work.

 

:[Three nearly identical panels showing the lower-left portion of a wheel and hub diagram with symbols and an equation, each with a different character holding a pointer up to the diagram and a label above the panel with the character's profession:]

 

:[Physicist Approximations]

:[Engineer Approximations]

 

:[Cosmologist Approximations]

 

[[Category:Astronomy]]