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-rw-r--r--CHANGELOG.txt7
-rw-r--r--html/encyclopedia/chemistry.html6
-rw-r--r--html/encyclopedia/mathematics.html86
-rw-r--r--html/encyclopedia/physics.html32
-rw-r--r--html/projects.html5
5 files changed, 79 insertions, 57 deletions
diff --git a/CHANGELOG.txt b/CHANGELOG.txt
index f651c69..855a3ec 100644
--- a/CHANGELOG.txt
+++ b/CHANGELOG.txt
@@ -1,3 +1,10 @@
+# 49
+
+* encyclopedia: Update mathematics page;
+* encyclopedia: Fix error on mathematics page;
+* encyclopedia: Update physics page;
+* encyclopedia: Fix error on physics page;
+
# 48
* Remove 'zapx' from projects page;
diff --git a/html/encyclopedia/chemistry.html b/html/encyclopedia/chemistry.html
index 5c70343..6763862 100644
--- a/html/encyclopedia/chemistry.html
+++ b/html/encyclopedia/chemistry.html
@@ -83,9 +83,9 @@
<td class="math">\(N_A\)</td>
</tr>
</table>
- <p class="math">\(M_u = m_uN_a \approx \frac{999\ 999\ 999\ 65}{10 ^ {14}}\ \frac{kg}{mol}\)</p>
- <p class="math">\(m_u = \frac{m(_6 ^ {12}C)}{12} \approx \frac{16\ 605\ 390\ 666}{10 ^ {37}}\ kg\)</p>
- <p class="math">\(N_A = 602\ 214\ 076 \cdot 10 ^ {15}\ mol ^ {-1}\)</p>
+ <p class="math">\(M_u = m_uN_a \approx \frac{999\ 999\ 999\ 65}{10^{14}}\ \frac{kg}{mol}\)</p>
+ <p class="math">\(m_u = \frac{m(_6^{12}C)}{12} \approx \frac{16\ 605\ 390\ 666}{10^{37}}\ kg\)</p>
+ <p class="math">\(N_A = 602\ 214\ 076 \cdot 10^{15}\ mol^{-1}\)</p>
</div>
</div>
<!--#include virtual="/include/pgftr.shtml"-->
diff --git a/html/encyclopedia/mathematics.html b/html/encyclopedia/mathematics.html
index e0c14d1..948183e 100644
--- a/html/encyclopedia/mathematics.html
+++ b/html/encyclopedia/mathematics.html
@@ -19,13 +19,17 @@
<p class="math">\(\frac{z}{y} = x\)</p>
<p class="math">\(\frac{z}{x} = y\)</p>
<br />
- <p class="math">\(x ^ y = z\)</p>
+ <p class="math">\(\frac{x}{y} = z\)</p>
+ <p class="math">\(zy = x\)</p>
+ <p class="math">\(\frac{x}{z} = y\)</p>
+ <br />
+ <p class="math">\(x^y = z\)</p>
<p class="math">\(\sqrt[y]{z} = x\)</p>
<p class="math">\(log_{x}(z) = y\)</p>
<br />
- <p class="math">\(x ^ n = \frac{1}{x ^ {-n}}, x \lt 0\)</p>
- <p class="math">\(x ^ 0 = 1\)</p>
- <p class="math">\(x ^ {\frac{a}{b}} = \sqrt[b]{x ^ a}\)</p>
+ <p class="math">\(x^n = \frac{1}{x^{-n}}, x \lt 0\)</p>
+ <p class="math">\(x^0 = 1\)</p>
+ <p class="math">\(x^{\frac{a}{b}} = \sqrt[b]{x^a}\)</p>
<br />
<p class="math">\(\frac{x}{y} = x\frac{1}{y}\)</p>
<p class="math">\(\frac{x}{y} + n = \frac{x + n y}{y}\)</p>
@@ -36,23 +40,23 @@
<p class="math">\(\frac{\frac{x}{y}}{z} = \frac{x}{yz}\)</p>
<p class="math">\(\frac{\frac{x}{y}}{\frac{a}{b}} = \frac{xb}{ya}\)</p>
<br />
- <p class="math">\(x ^ ax ^ b = x ^ {a + b}\)</p>
- <p class="math">\(\frac{x ^ a}{x ^ b} = x ^ {a - b}\)</p>
- <p class="math">\(x ^ ay ^ a = (xy) ^ a\)</p>
- <p class="math">\(\frac{x ^ a}{y ^ a} = (\frac{x}{y}) ^ a\)</p>
- <p class="math">\((x ^ a) ^ b = x ^ {ab}\)</p>
+ <p class="math">\(x^ax^b = x^{a + b}\)</p>
+ <p class="math">\(\frac{x^a}{x^b} = x^{a - b}\)</p>
+ <p class="math">\(x^ay^a = (xy)^a\)</p>
+ <p class="math">\(\frac{x^a}{y^a} = (\frac{x}{y})^a\)</p>
+ <p class="math">\((x^a)^b = x^{ab}\)</p>
</div>
<div class="section" id="equations">
<p class="large">Ligninger</p>
<p>Andengrads:</p>
- <p class="math">\(y = ax ^ 2 + bx + c\)</p>
+ <p class="math">\(ax^2 + bx + c = 0\)</p>
<p class="math">\(x = \frac{-b \pm \sqrt[2]{d}}{2a}\)</p>
- <p class="math">\(d = b ^ 2 - 4ac\)</p>
+ <p class="math">\(d = b^2 - 4ac\)</p>
</div>
<div class="section" id="functions">
<p class="large">Funktioner</p>
<p class="math">\(y = f(x)\)</p>
- <p class="math">\(x = f ^ {-1}(y)\)</p>
+ <p class="math">\(x = f^{-1}(y)\)</p>
<br />
<p>Lineær:</p>
<p class="math">\(f(x) = ax + b\)</p>
@@ -61,20 +65,20 @@
<p class="math">\(f(0) = b\)</p>
<br />
<p>Eksponentiel:</p>
- <p class="math">\(f(x) = ba ^ x\)</p>
+ <p class="math">\(f(x) = ba^x\)</p>
<p class="math">\(a = \sqrt[x_1 - x_0]{\frac{y_1}{y_{0}}}\)</p>
- <p class="math">\(b = \frac{y}{a ^ x}\)</p>
+ <p class="math">\(b = \frac{y}{a^x}\)</p>
<p class="math">\(f(0) = b\)</p>
<br />
<p>Potens:</p>
- <p class="math">\(f(x) = bx ^ a\)</p>
+ <p class="math">\(f(x) = bx^a\)</p>
<p class="math">\(a = \frac{log_n(y_1) - log_n(y_0)}{log_n(x_1) - log_n(x_1)}\)</p>
- <p class="math">\(b = \frac{y}{x ^ a}\)</p>
+ <p class="math">\(b = \frac{y}{x^a}\)</p>
<p class="math">\(f(0) = 0\)</p>
<p class="math">\(f(1) = b\)</p>
<br />
<p>Andengrads:</p>
- <p class="math">\(f(x) = ax ^ 2 + bx + c\)</p>
+ <p class="math">\(f(x) = ax^2 + bx + c\)</p>
</div>
<div class="section" id="trigonometry">
<p class="large">Trigonometri</p>
@@ -89,12 +93,12 @@
<p class="math">\(csc(\theta) = \frac{hypotenuse}{modliggende}\)</p>
<p class="math">\(sec(\theta) = \frac{hypotenuse}{hosliggende}\)</p>
<br />
- <p class="math">\(sin ^ {-1} (\frac{modliggende}{hypotenuse}) = \theta\)</p>
- <p class="math">\(cos ^ {-1} (\frac{hosliggende}{hypotenuse}) = \theta\)</p>
- <p class="math">\(tan ^ {-1} (\frac{modliggende}{hosliggende}) = \theta\)</p>
- <p class="math">\(cot ^ {-1} (\frac{hosliggende}{modliggende}) = \theta\)</p>
- <p class="math">\(csc ^ {-1} (\frac{hypotenuse}{modliggende}) = \theta\)</p>
- <p class="math">\(sec ^ {-1} (\frac{hypotenuse}{hosliggende}) = \theta\)</p>
+ <p class="math">\(sin^{-1} (\frac{modliggende}{hypotenuse}) = \theta\)</p>
+ <p class="math">\(cos^{-1} (\frac{hosliggende}{hypotenuse}) = \theta\)</p>
+ <p class="math">\(tan^{-1} (\frac{modliggende}{hosliggende}) = \theta\)</p>
+ <p class="math">\(cot^{-1} (\frac{hosliggende}{modliggende}) = \theta\)</p>
+ <p class="math">\(csc^{-1} (\frac{hypotenuse}{modliggende}) = \theta\)</p>
+ <p class="math">\(sec^{-1} (\frac{hypotenuse}{hosliggende}) = \theta\)</p>
<br />
<p>Forkortelser:</p>
<p class="math">\(sin = sinus\)</p>
@@ -103,12 +107,12 @@
<p class="math">\(cot = cotangens\)</p>
<p class="math">\(csc = cosekant\)</p>
<p class="math">\(sec = sekant\)</p>
- <p class="math">\(arcsin = sin ^ {-1}\)</p>
- <p class="math">\(arccos = cos ^ {-1}\)</p>
- <p class="math">\(arctan = tan ^ {-1}\)</p>
- <p class="math">\(arccot = cot ^ {-1}\)</p>
- <p class="math">\(arcsec = sec ^ {-1}\)</p>
- <p class="math">\(arccsc = csc ^ {-1}\)</p>
+ <p class="math">\(arcsin = sin^{-1}\)</p>
+ <p class="math">\(arccos = cos^{-1}\)</p>
+ <p class="math">\(arctan = tan^{-1}\)</p>
+ <p class="math">\(arccot = cot^{-1}\)</p>
+ <p class="math">\(arcsec = sec^{-1}\)</p>
+ <p class="math">\(arccsc = csc^{-1}\)</p>
<br />
<p class="math">\(deg(rad) = \frac{rad\pi}{180}\)</p>
<p class="math">\(rad(deg) = \frac{deg180}{\pi}\)</p>
@@ -116,8 +120,8 @@
<p class="math">\(vinkelsum(x) = (x - 2)\pi\)</p>
<p class="math">\(vinkelsum(3) = (3 - 2)\pi = \pi\)</p>
<br />
- <p class="math">\(\angle A = sin ^ {-1} (\frac{a}{c}) = cos ^ {-1} (\frac{b}{c}) = tan ^ {-1} (\frac{a}{b}) = vinkelsum(3) - \angle B - \angle C\)</p>
- <p class="math">\(\angle B = sin ^ {-1} (\frac{b}{c}) = cos ^ {-1} (\frac{a}{c}) = tan ^ {-1} (\frac{b}{a}) = vinkelsum(3) - \angle A - \angle C\)</p>
+ <p class="math">\(\angle A = sin^{-1} (\frac{a}{c}) = cos^{-1} (\frac{b}{c}) = tan^{-1} (\frac{a}{b}) = vinkelsum(3) - \angle B - \angle C\)</p>
+ <p class="math">\(\angle B = sin^{-1} (\frac{b}{c}) = cos^{-1} (\frac{a}{c}) = tan^{-1} (\frac{b}{a}) = vinkelsum(3) - \angle A - \angle C\)</p>
<p class="math">\(\angle C = vinkelsum(3) - \angle A - \angle B\)</p>
<p>I en regulær trekant:</p>
<p class="math">\(\angle A = \angle B = \angle C\)</p>
@@ -130,11 +134,11 @@
<p>I en regulær trekant:</p>
<p class="math">\(a = b = c\)</p>
<p>I en retvinklet trekant:</p>
- <p class="math">\(a = \sqrt[2]{c - b ^ 2}\)</p>
- <p class="math">\(b = \sqrt[2]{c - a ^ 2}\)</p>
- <p class="math">\(c = \sqrt[2]{a ^ 2 + b ^ 2}\)</p>
+ <p class="math">\(a = \sqrt[2]{c - b^2}\)</p>
+ <p class="math">\(b = \sqrt[2]{c - a^2}\)</p>
+ <p class="math">\(c = \sqrt[2]{a^2 + b^2}\)</p>
<p>I en retvinklet trekant, hvori kateterne har samme længde:</p>
- <p class="math">\(a = b = \sqrt[2]{\frac{c ^ 2}{2}}\)</p>
+ <p class="math">\(a = b = \sqrt[2]{\frac{c^2}{2}}\)</p>
<br />
<p class="math">\(O = a + b + c\)</p>
<p class="math">\(A = \frac{b h}{2}\)</p>
@@ -147,7 +151,7 @@
<p class="math">\(b_1 = b_0 k\)</p>
<p class="math">\(c_1 = c_0 k\)</p>
<p class="math">\(O_1 = O_0 k\)</p>
- <p class="math">\(A_1 = A_0 k ^ 2\)</p>
+ <p class="math">\(A_1 = A_0 k^2\)</p>
</div>
<div class="section" id="constants">
<p class="large">Konstanter</p>
@@ -181,12 +185,12 @@
<td class="math">\(\phi\)</td>
</tr>
</table>
- <p class="math">\(\sqrt[2]{2} \approx \frac{1\ 414\ 213\ 562}{10 ^ 9}\)</p>
- <p class="math">\(\sqrt[2]{3} \approx \frac{1\ 732\ 050\ 808}{10 ^ 9}\)</p>
- <p class="math">\(e = \sum_{n = 0} ^ \infty \frac{1}{n!} \approx \frac{2\ 718\ 281\ 828}{10 ^ 9}\)</p>
+ <p class="math">\(\sqrt[2]{2} \approx \frac{1\ 414\ 213\ 562}{10^9}\)</p>
+ <p class="math">\(\sqrt[2]{3} \approx \frac{1\ 732\ 050\ 808}{10^9}\)</p>
+ <p class="math">\(e = \sum_{n = 0}^\infty \frac{1}{n!} \approx \frac{2\ 718\ 281\ 828}{10^9}\)</p>
<p class="math">\(i = \sqrt[2]{-1}\)</p>
- <p class="math">\(\pi \approx \frac{3\ 141\ 592\ 654}{10 ^ 9}\)</p>
- <p class="math">\(\phi = \frac{1 + \sqrt[2]{5}}{2} \approx \frac{1\ 618\ 033\ 989}{10 ^ 9}\)</p>
+ <p class="math">\(\pi \approx \frac{3\ 141\ 592\ 654}{10^9}\)</p>
+ <p class="math">\(\phi = \frac{1 + \sqrt[2]{5}}{2} \approx \frac{1\ 618\ 033\ 989}{10^9}\)</p>
</div>
</div>
<!--#include virtual="/include/pgftr.shtml"-->
diff --git a/html/encyclopedia/physics.html b/html/encyclopedia/physics.html
index 780b7dc..b21b3c3 100644
--- a/html/encyclopedia/physics.html
+++ b/html/encyclopedia/physics.html
@@ -97,13 +97,13 @@
<td>areal</td>
<td class="math">\(A\)</td>
<td>kvadratmeter</td>
- <td class="math">\(m ^ 2\)</td>
+ <td class="math">\(m^2\)</td>
</tr>
<tr>
<td>acceleration</td>
<td class="math">\(a\)</td>
<td>meter pr. kvadratsekund</td>
- <td class="math">\(\frac{m}{s ^ 2}\)</td>
+ <td class="math">\(\frac{m}{s^2}\)</td>
</tr>
<tr>
<td>varmekapacitet</td>
@@ -127,7 +127,7 @@
<td>volumen</td>
<td class="math">\(V\)</td>
<td>kubikmeter</td>
- <td class="math">\(m ^ 3\)</td>
+ <td class="math">\(m^3\)</td>
</tr>
<tr>
<td>hastighed</td>
@@ -139,7 +139,7 @@
<td>densitet</td>
<td class="math">\(\rho\)</td>
<td>kilogram pr. kubikmeter</td>
- <td class="math">\(\frac{kg}{m ^ 3}\)</td>
+ <td class="math">\(\frac{kg}{m^3}\)</td>
</tr>
</table>
<p>Yderligere mål:</p>
@@ -180,14 +180,14 @@
<p class="large">Formler</p>
<p class="math">\(a = \frac{F}{m}\)</p>
<p>På en planet:</p>
- <p class="math">\(g = \frac{Gm}{r ^ {2}}\)</p>
+ <p class="math">\(g = \frac{Gm}{r^{2}}\)</p>
<p>... hvori <i>r</i> er afstanden til planetens kerne.</p>
- <p class="math">\(g = \frac{981}{100} \frac{m}{s ^ 2}\)</p>
+ <p class="math">\(g = \frac{981}{100} \frac{m}{s^2}\)</p>
<p>... er standard på Jorden.</p>
<br />
<p class="math">\(E = Fs\)</p>
<p class="math">\(E = Pt\)</p>
- <p class="math">\(K = \frac{mv ^ {2}}{2}\)</p>
+ <p class="math">\(K = \frac{mv^{2}}{2}\)</p>
<p class="math">\(Q = CT = cmT\)</p>
<p>Gravitation:</p>
<p class="math">\(U = Fs = mgs\)</p>
@@ -196,7 +196,7 @@
<p class="math">\(F = ma\)</p>
<p class="math">\(F = \frac{E}{s}\)</p>
<p>Gravtitation mellem to objekter:</p>
- <p class="math">\(F = \frac{Gm_{0}m_{1}}{r ^ {2}}\)</p>
+ <p class="math">\(F = \frac{Gm_{0}m_{1}}{r^{2}}\)</p>
<p>... <i>m_0</i> og <i>m_1</i> er masserne af objekterne og <i>r</i> er distancen mellem centrene af de to objekter.</p>
<br />
<p class="math">\(P = \frac{E}{t}\)</p>
@@ -232,14 +232,20 @@
</tr>
<tr>
<td>Boltzmanns konstant</td>
- <td class="math">\(k_b\)</td>
+ <td class="math">\(k_B\)</td>
+ </tr>
+ <tr>
+ <td>Stefan-Boltzmann konstanten</td>
+ <td class="math">\(\sigma\)</td>
</tr>
</table>
+ <p class="graphicText">Evt. se <a href="/html/encyclopedia/mathematics.html#constants">matematikkens konstanter</a>.</p>
<p class="math">\(c = 299\ 792\ 458\ \frac{m}{s}\)</p>
- <p class="math">\(e = \frac{1\ 602\ 176\ 634}{10 ^ {28}}\ C\)</p>
- <p class="math">\(G \approx \frac{66\ 743}{10 ^ {15}}\ \frac{m ^ 3}{kg \cdot s ^ 2}\)</p>
- <p class="math">\(h = \frac{662\ 607\ 015}{10 ^ {42}}\ \frac{J}{Hz}\)</p>
- <p class="math">\(k_b = \frac{1\ 380\ 649}{10 ^ {29}}\ \frac{J}{K}\)</p>
+ <p class="math">\(e = \frac{1\ 602\ 176\ 634}{10^{28}}\ C\)</p>
+ <p class="math">\(G \approx \frac{66\ 743}{10^{15}}\ \frac{m^3}{kg \cdot s^2}\)</p>
+ <p class="math">\(h = \frac{662\ 607\ 015}{10^{42}}\ \frac{J}{Hz}\)</p>
+ <p class="math">\(k_B = \frac{1\ 380\ 649}{10^{29}}\ \frac{J}{K}\)</p>
+ <p class="math">\(\sigma = \frac{2\pi^5k_B^4}{15h^3c^2} \approx \frac{5\ 670\ 374\ 419}{10^{17}}\)</p>
</div>
</div>
<!--#include virtual="/include/pgftr.shtml"-->
diff --git a/html/projects.html b/html/projects.html
index 50dbf01..4e922e8 100644
--- a/html/projects.html
+++ b/html/projects.html
@@ -39,3 +39,8 @@
<!--#include virtual="/include/pgftr.shtml"-->
</body>
</html>
+
+x/y = z
+z = x/y
+z = x * 1/y
+z / x = x
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-25 04:45:01 +0100