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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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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 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_. 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` We also use Magnitudes for _Dimensionless_ Units. `percent` has a Magnitude of :math:`1/100`, and
would have a Magnitude of $12$. `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 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: 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`). consider the ratio between `degrees` and `radians`).
3. We should _avoid overflow_ wherever possible (note that `std::intmax_t` can't even handle certain 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 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 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 a factor of :math:`\pi`. The arithmetic with _its floating point representation_ is unlikely to
_exactly_. cancel _exactly_.
Another common alternative choice is `std::ratio`, but this fails the first requirement: rational 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 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. we have a rational number, and they are compatible with how humans write numbers when we don't.
Example: 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>()`. `denominator(m1) == mag<25>()`.
- $m2 = \sqrt{m1}$. Then `numerator(m2) == mag<3>()`, and `denominator(m2) == mag<5>()`. Note that - :math:`m2 = \sqrt{m1}`. Then `numerator(m2) == mag<3>()`, and `denominator(m2) == mag<5>()`.
this is consistent with how humans would typically write `m2`, as $\frac{3\sqrt{3} \pi}{5}$. Note that this is consistent with how humans would typically write `m2`, as :math:`\frac{3\sqrt{3}
\pi}{5}`.
Getting values out Getting values out
------------------ ------------------