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Diffstat (limited to 'html')
| -rw-r--r-- | html/encyclopedia/chemistry.html | 6 | ||||
| -rw-r--r-- | html/encyclopedia/mathematics.html | 86 | ||||
| -rw-r--r-- | html/encyclopedia/physics.html | 32 | ||||
| -rw-r--r-- | html/projects.html | 5 |
4 files changed, 72 insertions, 57 deletions
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 |