 # Boost :

From: Andreas Harnack (ah.boost.03_at_[hidden])
Date: 2007-02-09 15:31:43

james.jones_at_[hidden] wrote:

> I suspect this idea, while clever, does not cover the problem domain sufficiently well to be superior to lists.

Please have a look at the attached list.
(I hope sending attachments works.)

This is a list of all SI units I could find on a quick search. The first
two columns are nominator and denominator a corresponding rational
number would have. Of course, this is not a proof, but the numbers
suggest that for practical purposes we're not even getting near a range
that's likely to be dangerous.

By the way, there's no need to worry about growing intermediate results:
a/b * c/d is equal to a/d * c/b and these two factors can be normalized
before the multiplication is carried out. If that's done and a/b and c/d
were in normal form, then so will be the result and there's no
intermediate result growing larger then the final product.

Andreas

9 1 3^2 m^2 area square metre m2
27 1 3^3 m^3 volume cubic metre m3
3 2 3/2 m/s speed, velocity metre per second m/s
3 4 3/2^2 m/s^2 acceleration metre per second squared m/s2
1 3 1/3 1/m wavenumber reciprocal metre m–1
5 27 5/3^3 kg/m^3 mass density kilogram per cubic metre kg/m3
5 9 5/3^2 kg/m^2 surface density kilogram per square metre kg/m2
27 5 3^3/5 m^3/kg specific volume cubic metre per kilogram m3/kg
7 9 7/3^2 A/m^2 current density ampere per square metre A/m2
7 3 7/3 A/m magnetic field strength ampere per metre A/m
13 27 13/3^3 mol/m^3 concentration mole per cubic metre mol/m3
5 27 5/3^3 kg/m^3 mass concentration kilogram per cubic metre kg/m3
17 9 17/3^2 cd/m^2 luminance candela per square metre cd/m2

1 2 1/2 1/s frequency hertz (d) Hz
15 4 5*3/2^2 kg*m/s^2 force newton N
5 12 5/(3*2^2) kg/m*s^2 pressure, stress pascal Pa N/m2
45 4 5*3^2/2^2 kg*m^2/s^2 energy, work, heat joule J N m
45 8 5*3^2/2^3 kg*m^2/s^3 power, radiant flux watt W J/s
14 1 7*2 A*s electric charge coulomb C
45 56 5*3^2/(7*2^3) kg*m^2/A*s^3 electric potential volt V W/A
784 45 7^2*2^4/(5*3^2) A^2*s^4/kg*m^2 capacitance farad F C/V
45 392 5*3^2/(7^2*2^3) kg*m^2/A^2*s^3 electric resistance ohm V/A
392 45 7^2*2^3/(5*3^2) A^2*s^3/kg*m^2 electric conductance siemens S A/V
45 28 5*3^2/(7*2^2) kg*m^2/A*s^2 magnetic flux weber Wb V s
5 28 5/(7*2^2) kg/A*s^2 magnetic flux density tesla T Wb/m2
45 196 5*3^2/(7^2*2^2) kg*m^2/A^2*s^2 inductance henry H Wb/A
11 1 11 K Celsius temperature degree Celsius (e) °C
17 1 17 cd luminous flux lumen lm cd sr (c)
17 9 17/3^2 cd/m^2 illuminance lux lx lm/m2
1 2 1/2 1/s activity referred to a radionuclide (f) becquerel (d) Bq
9 4 3^2/2^2 m^2/s^2 absorbed dose, specific energy (imparted), kerma gray Gy J/kg

5 6 5/(3*2) kg/m*s dynamic viscosity pascal second Pa s
45 4 5*3^2/2^2 kg*m^2/s^2 moment of force newton metre N m
5 4 5/2^2 kg/s^2 surface tension newton per metre N/m
5 8 5/2^3 kg/s^3 heat flux density, watt per square metre W/m2
45 44 5*3^2/(11*2^2) kg*m^2/K*s^2 heat capacity, entropy joule per kelvin J/K
9 44 3^2/(11*2^2) m^2/K*s^2 specific heat capacity, joule per kilogram kelvin J/(kg K)
9 4 3^2/(2^2) m^2/s^2 specific energy joule per kilogram J/kg
15 88 5*3/(11*2^3) kg*m/K*s^3 thermal conductivity watt per metre kelvin W/(m K)
5 12 5/(3*2^2) kg/m*s^2 energy density joule per cubic metre J/m3
15 56 5*3/(7*2^3) kg*m/A*s^3 electric field strength volt per metre V/m
14 27 7*2/(3^3) A*s/m^3 electric charge density coulomb per cubic metre C/m3
14 9 7*2/3^2 A*s/m^2 surface charge density coulomb per square metre C/m2
14 9 7*2/3^2 A*s/m^2 electric flux density, coulomb per square metre C/m2
784 135 7^2*2^4/(5*3^3) A^2*s^4/kg*m^3 permittivity farad per metre F/m
15 196 5*3/(7^2*2^2) kg*m/A^2*s^2 permeability henry per metre H/m
45 52 5*3^2/(13*2^2) kg*m^2/mol*s^2 molar energy joule per mole J/mol
45 572 5*3^2/(13*11*2^2) kg*m^2/mol*K*s^2 molar entropy joule per mole kelvin J/(mol K)
14 5 7*2/5 A*s/kg exposure coulomb per kilogram C/kg
9 8 3^2/2^3 m^2/s^3 absorbed dose rate gray per second Gy/s
13 54 13/(3^3*2) mol/m^3*s catalytic activity katal per cubic metre kat/m3