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- a point <math>C</math> in <math>\mathcal{S}</math> such that <math>AC=BC</math>. We say tha ...tre-free</i> if for any three points <math>A</math>, <math>B</math>, <math>C</math> in4 KB (709 words) - 14:00, 1 June 2024
- ...math>(p-1)! + 1</math> is divisible by <math>p</math> if and only if <math>p</math> is prime. It was stated by John Wilson. The French mathematician Lag ...<math>(p-1)! + 1</math>. Therefore <math>p</math> does not divide <math>(p-1)! + 1</math>.4 KB (639 words) - 00:53, 2 February 2023
- ...(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})+c-\frac{b^2}{4a} = a(x+\frac{b}{2a})^2+c-\frac{b^2}{4a}.</cmath> ...\frac{b^2}{4a}</math> if <math>a</math> is positive and <math>ax^2+bx+c\le c-\frac{b^2}{4a}</math> if <math>a</math> is negative.3 KB (583 words) - 20:20, 2 August 2024
- ...generally concerned with finding the number of combinations of size <math>r</math> from an original set of size <math>n</math> The common forms of denoting the number of combinations of <math>{r}</math> objects from a set of <math>{n}</math> objects is:4 KB (638 words) - 20:55, 5 January 2025
- ...rrightarrow{v}</math> and <math>\overrightarrow{w}</math> in <math>\mathbb{R}^n</math>, where <math>\overrightarrow{v} \cdot \overrightarrow{w}</math> i ...ce]], and let <math> \langle \cdot, \cdot \rangle : V \times V \to \mathbb{R} </math> be an [[inner product]]. Then for any <math> \mathbf{a,b} \in V <13 KB (2,048 words) - 14:28, 22 February 2024
- ...C</math>, <math>Q</math> is on the extension of <math>AC</math>, and <math>R</math> on the intersection of <math>PQ</math> and <math>AB</math>, then pair A=(7,6), B=(0,0), C=(10,0), P=(4,0), Q=(6,8), R;5 KB (804 words) - 02:01, 12 June 2023
- ...ibility|divisible]] by <math>{p}</math>, then <math>a^{p-1}\equiv 1 \pmod {p}</math>. ...to restrict ourselves to integers <math>{a}</math> not divisible by <math>{p}</math>.16 KB (2,660 words) - 22:42, 28 August 2024
- ...ith sides of length <math>a \leq b \leq c</math> we have <math>a^2 + b^2 = c^2</math>. The Inequality extends this to [[obtuse triangle| obtuse]] and [ ...an obtuse triangle with sides <math>a \leq b \leq c</math>, <math>a^2+b^2<c^2</math>.7 KB (1,300 words) - 00:11, 28 October 2024
- ...[cyclic quadrilateral]] <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[diagonal]]s <math>{e},{f}</math>: Given cyclic quadrilateral <math>ABCD,</math> extend <math>CD</math> to <math>P</math> such that <math>\angle BAC=\angle DAP.</math>6 KB (922 words) - 16:34, 13 January 2025
- ...g <math>P+Q+R=\mathcal{O}</math> if and only if <math>P,Q</math> and <math>R</math> lie on a line. <cmath>G_k(z)=\sum_{(c,d)\in Z^2\backslash 0} (cz+d)^{-k}</cmath>5 KB (849 words) - 15:14, 18 May 2021
- ...<math>\mathbb{R}</math>, is a subset of [[complex number]]s(<math>\mathbb{C}</math>). Commonly used subsets of the real numbers are the [[rational numb ==The set <math>\mathbb{R}~</math>==3 KB (496 words) - 22:22, 5 January 2022
- * if <math>(a,b)\in f</math> and <math>(a,c)\in f</math> then <math>b=c</math>. (Here <math>(a,b)</math> is an [[ordered pair]].) ...ective (and therefore bijective) from <math>\mathbb{C} \rightarrow \mathbb{C}</math>.10 KB (1,761 words) - 02:16, 12 May 2023
- ...the [[distance formula]], this gives <math>\sqrt{(x - h)^2 + (y - k)^2} = r</math> which is more commonly written as <cmath>(x - h)^2 + (y - k)^2 = r^2.</cmath>9 KB (1,510 words) - 18:56, 16 January 2025
- '''Muirhead's Inequality''' states that if a sequence <math>p</math> [[Majorization|majorizes]] a sequence <math>q</math>, then given a s Given <math>p=(p_1,p_2,\ldots,p_n)\in\mathbb{R}^n</math>, let's write8 KB (1,346 words) - 11:53, 8 October 2023
- Every vector <math>\overrightarrow{PQ}</math> has a starting point <math>P\langle x_1, y_1\rangle</math> and an endpoint <math>Q\langle x_2, y_2\rangl pen p=linewidth(1);11 KB (1,875 words) - 14:35, 7 January 2025
- ...te it as <math>z=r(\cos\theta+i\sin\theta)=r cis\theta</math>, where <math>r=|z| = \sqrt{a^2 + b^2}</math>. By [[Euler's identity|Euler's formula]], wh pair A,B,C,D,E;1 KB (238 words) - 21:51, 20 February 2022
- ...r and closer to <math>x</math>, we may have to use larger and larger <math>p</math> and <math>q</math>. So, the reasonable question to ask here is how w ...number <math>x</math> can be approximated by a rational number <math>\frac{p}{q}</math> with a given denominator <math>q\ge 1</math> with an error not e7 KB (1,290 words) - 11:18, 30 May 2019
- pair O=(0,0),A=(-1,0),B=(0,1),C=(1,0),P=(1/2,0),Q=(1/2,sqrt(3)/2),R=foot(P,Q,O); draw(B--O--C--arc(O,C,A)--O--R--P); rightanglemark(O,P,R);5 KB (913 words) - 14:44, 14 August 2024
- ...s, every polynomial over <math>\mathbb{C}</math> splits over <math>\mathbb{C}</math>, or decomposes into linear factors. ...oss of generality, suppose that <math>P</math> is [[monic]]. Then <math>1/P(z)</math> is an [[entire]] function; we wish to show that it is bounded. I5 KB (832 words) - 13:22, 11 January 2024
- <math>\mathbb{P}</math>: Also an ambiguous notation, use for the positive [[prime]]s or the <math>\mathbb{R}</math>: the [[real]]s (a field).8 KB (1,401 words) - 16:49, 10 January 2025