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Fix math notation in magnitude doc

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Chip Hogg
2022-08-10 01:14:12 +00:00
parent 8076ecf50f
commit d0325da46a
1 changed files with 9 additions and 8 deletions
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17
docs/framework/magnitudes.rst
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@@ -6,8 +6,8 @@ Magnitudes
The ratio of two Units of the same Dimension---say, `inches` and `centi<meters>`---is some constant
number, which is known at compile time. It's a positive real number---a _Magnitude_.
We also use Magnitudes for _Dimensionless_ Units. `percent` has a Magnitude of $1/100$, and `dozen`
would have a Magnitude of $12$.
We also use Magnitudes for _Dimensionless_ Units. `percent` has a Magnitude of :math:`1/100`, and
`dozen` would have a Magnitude of :math:`12`.
Interestingly, it turns out that the usual numeric types are not up to this task. We need
a Magnitude representation that can do everything Units can do. This means, among other things:
@@ -19,12 +19,12 @@ a Magnitude representation that can do everything Units can do. This means, amo
consider the ratio between `degrees` and `radians`).
3. We should _avoid overflow_ wherever possible (note that `std::intmax_t` can't even handle certain
simple SI prefixes, such as `yotta`, representing $10^{24}$).
simple SI prefixes, such as `yotta`, representing :math:`10^{24}`).
Integers' inadequacies are clear enough, but even floating point falls short. Imagine if we
implemented all angular units in terms of `radians`: then both `degrees` and `revolutions` pick up
a factor of $\pi$. The arithmetic with _its floating point representation_ is unlikely to cancel
_exactly_.
a factor of :math:`\pi`. The arithmetic with _its floating point representation_ is unlikely to
cancel _exactly_.
Another common alternative choice is `std::ratio`, but this fails the first requirement: rational
numbers are ([rather infamously](https://hsm.stackexchange.com/a/7)!) _not_ closed under rational
@@ -84,10 +84,11 @@ Why these particular definitions? Because they are equivalent to the numerator
we have a rational number, and they are compatible with how humans write numbers when we don't.
Example:
- $m1 = \frac{27 \pi^2}{25}$. Then `numerator(m1) == mag<27>()`, and
- :math:`m1 = \frac{27 \pi^2}{25}`. Then `numerator(m1) == mag<27>()`, and
`denominator(m1) == mag<25>()`.
- $m2 = \sqrt{m1}$. Then `numerator(m2) == mag<3>()`, and `denominator(m2) == mag<5>()`. Note that
this is consistent with how humans would typically write `m2`, as $\frac{3\sqrt{3} \pi}{5}$.
- :math:`m2 = \sqrt{m1}`. Then `numerator(m2) == mag<3>()`, and `denominator(m2) == mag<5>()`.
Note that this is consistent with how humans would typically write `m2`, as :math:`\frac{3\sqrt{3}
\pi}{5}`.
Getting values out
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