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Diffstat (limited to 'html/encyclopedia')
| -rw-r--r-- | html/encyclopedia/latin.html | 5 | ||||
| -rw-r--r-- | html/encyclopedia/mathematics.html | 110 | ||||
| -rw-r--r-- | html/encyclopedia/physics.html | 2 |
3 files changed, 72 insertions, 45 deletions
diff --git a/html/encyclopedia/latin.html b/html/encyclopedia/latin.html index 25ab438..4f4ca64 100644 --- a/html/encyclopedia/latin.html +++ b/html/encyclopedia/latin.html @@ -8,7 +8,6 @@ <div class="section" id="roman-numerals"> <p class="large">Romertal</p> <p>Romertal er den primære måde at udtrykke tal i latin, samt andre europæiske sprog op til skiftet til arabertal. Romertal bruger tegn fra det latinske alfabet til at udtrykke værdier. Det bruger ikke cifre (i modsætning til arabertal).</p> - <br /> <table> <tr> <th>Tegn</th> @@ -47,7 +46,6 @@ <td class="rightAligne">1000</td> </tr> </table> - <br /> <p><sup>†</sup><sub> Per konvention.</sub></p> <p>For at udtrykke talværdier uden et tilsvarende tegn, så opstiller man dem som en kombination af tegn. Skriver man et mindre tegn (lige) før et større, så trækkes det mindre fra det større. Står det største først, så lægges de sammen.</p> <br /> @@ -148,7 +146,6 @@ <td>amā <b>buntur</b></td> </tr> </table> - <br /> <table> <tr class="small"> <th colspan="2">Imperandī</th> @@ -279,9 +276,7 @@ <td>rex <b>ibus</b></td> </tr> </table> - <br /> <p>Nogle substantiver (f.eks. <i>vīrus</i>) er uregelmæssige i henhold til de tidligere regler. Følgende er et skema over disse (endelser i kursiv er uregelmæssige):</p> - <br /> <table> <tr class="small"> <th></th> diff --git a/html/encyclopedia/mathematics.html b/html/encyclopedia/mathematics.html index 2cf20d4..426e717 100644 --- a/html/encyclopedia/mathematics.html +++ b/html/encyclopedia/mathematics.html @@ -19,27 +19,61 @@ <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">\(x ^ y = z\)</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">\(x ^ {a} x ^ {b} = x ^ {a + b}\)</p> - <p class="math">\(\frac{x ^ {a}}{x ^ {b}} = x ^ {a - b}\)</p> - <p class="math">\(x ^ {a} y ^ {a} = (x y) ^ {a}\)</p> - <p class="math">\(\frac{x ^ {a}}{y ^ {a}} = (\frac{x}{y}) ^ {a}\)</p> - <p class="math">\((x ^ {a}) ^ {b} = x ^ {a b}\)</p> - <br /> - <p class="math">\(\frac{x}{y} = x \frac{1}{y}\)</p> + <p class="math">\(\frac{x}{y} = x \cdot \frac{1}{y}\)</p> <p class="math">\(\frac{x}{y} + n = \frac{x + n y}{y}\)</p> <p class="math">\(\frac{x}{y} + \frac{a}{b} = \frac{x b + a y}{y b}\)</p> <p class="math">\(\frac{x}{y} n = \frac{x n}{y}\)</p> <p class="math">\(\frac{x}{y} \frac{a}{b} = \frac{x a}{y b}\)</p> + <p class="math">\(\frac{x}{\frac{a}{b}} = \frac{xb}{a}\)</p> <p class="math">\(\frac{\frac{x}{y}}{z} = \frac{x}{yz}\)</p> <p class="math">\(\frac{\frac{x}{y}}{\frac{a}{b}} = \frac{x b}{y a}\)</p> + <br /> + <p class="math">\(x ^ a x ^ b = x ^ {a + b}\)</p> + <p class="math">\(\frac{x ^ a}{x ^ b} = x ^ {a - b}\)</p> + <p class="math">\(x ^ a y ^ a = (x y) ^ a\)</p> + <p class="math">\(\frac{x ^ a}{y ^ a} = (\frac{x}{y}) ^ a\)</p> + <p class="math">\((x ^ a) ^ b = x ^ {a b}\)</p> + </div> + <div class="section" id="equations"> + <p class="large">Ligninger</p> + <p>Andengrads:</p> + <p class="math">\(y = a x ^ 2 + b x + c\)</p> + <p class="math">\(x = \frac{-b \pm \sqrt[2]{d}}{2a}\)</p> + <p class="math">\(d = b ^ 2 - 4 a c\)</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> + <br /> + <p>Lineær:</p> + <p class="math">\(f(x) = a x + b\)</p> + <p class="math">\(a = \frac{y_1 - y_0}{x_1 - x_0}\)</p> + <p class="math">\(b = y - ax\)</p> + <p class="math">\(b = f(0) = 0a + b\)</p> + <br /> + <p>Eksponentiel:</p> + <p class="math">\(f(x) = b a ^ x\)</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">\(b = f(0) = b a ^ 0 = 1b\)</p> + <br /> + <p>Potens:</p> + <p class="math">\(f(x) = b x ^ a\)</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">\(b = f(1) = b \cdot 1 ^ a = 1b\)</p> + <br /> + <p>Kvadratisk (andengrads):</p> + <p class="math">\(f(x) = a x ^ 2 + b x + c\)</p> </div> <div class="section" id="trigonometry"> <p class="large">Trigonometri</p> @@ -47,14 +81,6 @@ <p class="math">\(hosliggende_{\angle A} = modliggende_{\angle B} = b\)</p> <p class="math">\(hypotenuse = modliggende_{\angle C} = c\)</p> <br /> - <p>Forkortelser:</p> - <p class="math">\(sin_{sinus}\)</p> - <p class="math">\(cos_{cosinus}\)</p> - <p class="math">\(tan_{tangens}\)</p> - <p class="math">\(cot_{cotangens}\)</p> - <p class="math">\(csc_{cosekant}\)</p> - <p class="math">\(sec_{sekant}\)</p> - <br /> <p class="math">\(sin(\theta) = \frac{modliggende}{hypotenuse}\)</p> <p class="math">\(cos(\theta) = \frac{hosliggende}{hypotenuse}\)</p> <p class="math">\(tan(\theta) = \frac{modliggende}{hosliggende}\)</p> @@ -62,7 +88,6 @@ <p class="math">\(csc(\theta) = \frac{hypotenuse}{modliggende}\)</p> <p class="math">\(sec(\theta) = \frac{hypotenuse}{hosliggende}\)</p> <br /> - <p class="math">\(x = f ^ {-1} (f(x))\)</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> @@ -70,6 +95,13 @@ <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> + <p class="math">\(cos = cosinus\)</p> + <p class="math">\(tan = tangens\)</p> + <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> @@ -77,11 +109,11 @@ <p class="math">\(arcsec = sec ^ {-1}\)</p> <p class="math">\(arccsc = csc ^ {-1}\)</p> <br /> - <p class="math">\(deg(rad) = \frac{x}{\frac{\pi}{180}}\)</p> - <p class="math">\(rad(deg) = \frac{x}{\frac{180}{\pi}}\)</p> + <p class="math">\(deg(rad) = \frac{\pi x}{180}\)</p> + <p class="math">\(rad(deg) = \frac{180x}{\pi}\)</p> <br /> <p class="math">\(vinkelsum(x) = \pi(x - 2)\)</p> - <p class="math">\(vinkelsum(3) = \pi(3 - 2) = \pi(1) = \pi\)</p> + <p class="math">\(vinkelsum(3) = \pi(3 - 2) = \pi\)</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> @@ -91,30 +123,30 @@ <p>I en retvinklet trekant:</p> <p class="math">\(\angle C = \frac{\pi}{2}\)</p> <br /> - <p class="math">\(a = c ⋅ sin(\angle A) = c ⋅ cos(\angle B) = b ⋅ tan(\angle A) = b ⋅ cot(\angle B)\)</p> - <p class="math">\(b = c ⋅ sin(\angle B) = c ⋅ cos(\angle A) = a ⋅ tan(\angle B) = a ⋅ cot(\angle A)\)</p> - <p class="math">\(c = a ⋅ csc(\angle A) = b ⋅ csc(\angle B) = a ⋅ sec(\angle B) = b ⋅ sec(\angle A)\)</p> + <p class="math">\(a = c \cdot sin(\angle A) = c \cdot cos(\angle B) = b \cdot tan(\angle A) = b \cdot cot(\angle B)\)</p> + <p class="math">\(b = c \cdot sin(\angle B) = c \cdot cos(\angle A) = a \cdot tan(\angle B) = a \cdot cot(\angle A)\)</p> + <p class="math">\(c = a \cdot csc(\angle A) = b \cdot csc(\angle B) = a \cdot sec(\angle B) = b \cdot sec(\angle A)\)</p> <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> <p>Mellem to ligedannede trekanter:</p> - <p class="math">\(\angle A_{1} = \angle A_{0}\)</p> - <p class="math">\(\angle B_{1} = \angle B_{0}\)</p> - <p class="math">\(\angle C_{1} = \angle C_{0}\)</p> - <p class="math">\(k = \frac{a_{1}}{a_{0}} = \frac{b_{1}}{b_{0}} = \frac{c_{1}}{c_{0}}\)</p> - <p class="math">\(a_{1} = a_{0} k\)</p> - <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">\(\angle A_1 = \angle A_0\)</p> + <p class="math">\(\angle B_1 = \angle B_0\)</p> + <p class="math">\(\angle C_1 = \angle C_0\)</p> + <p class="math">\(k = \frac{a_1}{a_0} = \frac{b_1}{b_0} = \frac{c_1}{c_0}\)</p> + <p class="math">\(a_1 = a_0 k\)</p> + <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> </div> </div> <!--#include virtual="/include/pgftr.shtml"--> diff --git a/html/encyclopedia/physics.html b/html/encyclopedia/physics.html index c872246..bd9ec66 100644 --- a/html/encyclopedia/physics.html +++ b/html/encyclopedia/physics.html @@ -96,7 +96,7 @@ <p class="math">\(K = \frac{mv ^ {2}}{2}\)</p> <p class="math">\(Q = C \Delta T = c m \Delta T\)</p> <p>Gravitation:</p> - <p class="math">\(U = m h g\)</p> + <p class="math">\(U = m g h\)</p> <p>... hvori <i>g</i> er den lokale tyngeacceleration.</p> </div> </div> |