commit: 18b55f2fb4118872119dd6b588d36c7f8043191e
parent: d1344350842af60c2564fec2ccf2790110d8d3f6
author: Chris Noxz <chris@noxz.tech>
date: Sat, 21 Sep 2019 16:15:39 +0200
More maths!
3 files changed, 114 insertions(+), 8 deletions(-)
diff --git a/noxz.tech/guides/groff/index.md b/noxz.tech/guides/groff/index.md
@@ -56,7 +56,7 @@ Then use it like this:
[...]
.LP
- Calculate the sum of #-4# och #-7#
+ Calculate the sum of #-4# and #-7#
.sp 1
.RS
# (-4) + (-7) #
diff --git a/noxz.tech/guides/mathematics/index.md b/noxz.tech/guides/mathematics/index.md
@@ -8,10 +8,90 @@ out there.
{:: class="toc"}
{- class="toc-title"}Contents{--}
-+ 1 [Fractions](#math-fractions)
- + 1.1 [The fraction flip when dividing](#math-fractions-flip)
++ 1 [Divisibility rules](#math-div-rules)
+ + 1.1 [Divisibility by 2](#math-div-rules-2)
++ 2 [Fractions](#math-fractions)
+ + 2.1 [The fraction flip when dividing](#math-fractions-flip)
{::}
+{- id="math-div-rules"}Divisibility rules{--}
+---------------------------------------------
+When it comes to divisibility there exists some neat methods to test a certain
+number's different divisibilities, or factors. Following are those methods and
+their proof.
+
+### {- id="math-div-rules-2"}Divisibility by 2{--}
+It's common knowledge that every even number (numbers ending with an even
+number) is divisible by 2. This is because even numbers are multiples of 2. In
+short, if a number ends with either 0, 2, 4, 6 or 8 it is divisible by 2.
+
+Say we have a number
+{- class="math"}{- class="variable"}xyz{--}{--}, where
+ {- class="math"}{- class="variable"}x{--}{--} represents the number of
+ hundreds,
+ {- class="math"}{- class="variable"}y{--}{--} the number of tens and
+ {- class="math"}{- class="variable"}z{--}{--} the number of ones. This number
+ can be represented as
+{- class="math"}
+..{- class="equation"}
+....{-}100{--}
+....{- class="variable"}x{--}
+....{- class="operator"}+{--}
+....{-}10{--}
+....{- class="variable"}y{--}
+....{- class="operator"}+{--}
+....{- class="variable"}z{--}
+..{--}
+{--}. If {- class="math"}{- class="variable"}z{--}{--} is divisible by 2 we can
+ represent it as an even number
+{- class="math"}
+..{- class="equation"}
+....{-}2{--}
+....{- class="variable"}n{--}
+..{--}
+{--}, like so:
+
+{- class="math block"}
+..{- class="equation"}
+....{-}100{--}
+....{- class="variable"}x{--}
+....{- class="operator"}+{--}
+....{-}10{--}
+....{- class="variable"}y{--}
+....{- class="operator"}+{--}
+....{-}2{--}
+....{- class="variable"}n{--}
+..{--}
+..{- class="operator"}={--}
+..{- class="equation"}
+....{-}2{--}
+....{- class="fenced parenthesis"}
+......{-}50{--}
+......{- class="variable"}x{--}
+......{- class="operator"}+{--}
+......{-}5{--}
+......{- class="variable"}y{--}
+......{- class="operator"}+{--}
+......{- class="variable"}n{--}
+....{--}
+..{--}
+{--}
+
+{- class="math block"}
+..{- class="operator"}→{--}
+..{- class="equation"}
+....{-}2{--}
+....{- class="operator"}∣{--}
+....{- class="variable"}xyz{--}
+..{--}
+..{- class="operator"}⇔{--}
+..{- class="equation"}
+....{-}2{--}
+....{- class="operator"}∣{--}
+....{- class="variable"}z{--}
+..{--}
+{--}
+
{- id="math-fractions"}Fractions{--}
------------------------------------
@@ -33,7 +113,7 @@ We start of with the division of
....{-}5{--}
..{--}
{--}. From there we can reconstruct the two fractions as the dividend over
-the divisor with a horizontal line, for simplicity's sake, like so:
+ the divisor with a horizontal line, for simplicity's sake, like so:
{- class="math block"}
..{- class="fraction"}
diff --git a/noxz.tech/pub/style.css b/noxz.tech/pub/style.css
@@ -256,8 +256,7 @@ ul.repo-log li .log-date {
/* math extensions (alternative to MathML) */
.math {
font-family : monospace;
- /*font-size : 1em;
- line-height : 1.6em;*/
+ font-size : 1.1em;
}
.math.block {
@@ -275,6 +274,21 @@ ul.repo-log li .log-date {
visibility : hidden;
}
+.math .variable {
+ vertical-align : middle;
+ font-style : italic;
+ padding : 0;
+}
+
+.math .equation {
+ vertical-align : middle;
+ padding : 0 2px;
+}
+
+.math .equation>* {
+ vertical-align : middle;
+}
+
.math .operator {
font-family : "Latin Modern Math", "STIX Two Math", "XITS Math",
"STIX Math", "Libertinus Math", "TeX Gyre Termes Math",
@@ -283,11 +297,23 @@ ul.repo-log li .log-date {
"Asana Math", "Cambria Math", "Lucida Bright Math",
"Minion Math", STIXGeneral, STIXSizeOneSym, Symbol,
"Times New Roman", serif;
- /*font-size : 1em;*/
+ font-size : 0.9em;
padding : 0 2px;
vertical-align : middle;
}
+.math .fenced {
+ padding : 0 0.4em;
+ margin : 0 0.2em;
+}
+
+.math .fenced.parenthesis {
+ border-radius : 3px;
+ border : 1px solid #444;
+ border-top : none;
+ border-bottom : none;
+}
+
.math .fraction,
.math .fraction>span:first-child,
.math .fraction>span:last-child {
@@ -302,5 +328,5 @@ ul.repo-log li .log-date {
.math .fraction>span:last-child {
display : block;
- border-top : 1px solid #000000;
+ border-top : 1px solid #444;
}
