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- ===Proof with Similar Triangles=== ===Proof with [[Barycentric coordinates]]===5 KB (804 words) - 02:01, 12 June 2023
- === Coordinate Definition === ...circle, we can find the general form of the equation of a circle on the [[coordinate plane]] given its radius, <math>r</math>, and center <math>(h,k)</math>. W9 KB (1,585 words) - 12:46, 2 September 2024
- ...every fourth power, is either <math>1</math> or <math>0\mod 4</math>. The proof of this is fairly simple, and you can show it yourself. === Coordinate Plane ===9 KB (1,434 words) - 00:15, 4 July 2024
- ==Proof via Dirichlet's simultaneous [[rational approximation]] theorem== ...an choose a positive integer <math>q</math> such that the product of every coordinate of every vertex of every square in our partition becomes almost an integer2 KB (333 words) - 12:50, 26 June 2006
- ...the apex of the angle is not on the parallel lines. Set up a [[coordinate proof]].4 KB (709 words) - 00:50, 10 January 2022
- ...llinear, you can prove it (but that is already given in the later section [Proof that R,A, and B are collinear]). Drop a perpendicular from <math>P</math> t ===Full Proof that R, A, B are collinear ===14 KB (2,351 words) - 20:06, 8 December 2024
- ...ter <math>AO</math>, where <math>O</math> is the center of the circle. The proof is simple: every midpoint of a chord is a dilation of the endpoint with sca === Solution 4 (coordinate geometry) ===20 KB (3,497 words) - 14:37, 27 May 2024
- ...which the first coordinate of each pair after the first equals the second coordinate of the immediately preceding pair, and in which <math>(i,j)</math> and <mat .... In this case, the second coordinate of the final domino equals the first coordinate of the first domino.9 KB (1,659 words) - 17:35, 20 June 2024
- In the Cartesian coordinate system, an equation of the form <math>(x-h)^2+(y-k)^2=1</math> defines a un ...ems of [[trigonometry]]: <math>\sin^2{\theta}+\cos^2{\theta}=1</math>. The proof is as follows:2 KB (343 words) - 05:20, 25 November 2007
- ...application of the [[Pythagorean Theorem]] in the setting of a [[Cartesian coordinate system]]. In the two-dimensional case, it says that the distance between t ===Proof===2 KB (340 words) - 20:37, 1 August 2024
- ==Proof Centroid Lies on Euler Line== This proof utilizes the concept of [[spiral similarity]], which in this case is a [[ro59 KB (10,203 words) - 03:47, 30 August 2023
- ...lygon]], all of whose [[vertex | vertices]] are [[lattice points]] in a [[coordinate plane]], in terms of the number of lattice points inside the polygon and th == Proof ==7 KB (1,253 words) - 15:11, 14 September 2024
- ...e integers which cannot be expressed in the form <math>am + bn</math>. The proof is based on the fact that in each pair of the form <math>(k, mn-m-n-k)</mat ==Proof Without Words==17 KB (2,823 words) - 22:06, 15 November 2024
- ...ath> and <math>\boxed{020592}</math> cannot both be used.) Determine, with proof, the maximum number of distinct license plates that the state can use. ...9\}^6 </math> (hypercube), there are no collinear points (parallel to the coordinate axes).4 KB (565 words) - 01:21, 25 May 2024
- ...> is tangent to <math>\overline{BC}</math> at the point <math>D_2</math>. (Proof: let the points of tangency of the excircle with the lines <math>BC, AB, AC Proof: Let <math>I</math> be the center of circle <math>\omega</math>, i.e., <mat11 KB (2,091 words) - 07:35, 16 November 2017
- In connection with proof in geometry, indicate which one of the following statements is ''incorrect' <math> \textbf{(C)}\ \text{Every term used in a proof must have been defined previously.} </math>23 KB (3,646 words) - 20:53, 21 June 2024
- ...ula for finding the [[area]] of a simple [[polygon]] given the [[Cartesian coordinate system|coordinates]] of its [[vertex|vertices]]. ==Proof 1==8 KB (1,360 words) - 17:09, 28 September 2024
- ..., there is a cute proof that they all must weigh the same. Can you find a proof? Can you find a way to extend the result to the general case where the ball ...aving the smallest zero. If all balls weigh the same, we are done with the proof; if not, at least some of the integers must be positive. Now, we divide the4 KB (759 words) - 05:27, 18 July 2009
- ...p. She falls asleep and dreams of walking around a <math>2-\text{D}</math> coordinate grid, looking for a wormhole that she believes will transport her to the be ...to prove it, so he takes it to Michael who confirms Joshua's answer with a proof.71 KB (11,749 words) - 11:39, 20 November 2024
- ...th>p_{\frac{n}{2}+1}p_{\frac{n}{2}+2}</math>. To obtain the <math>y</math>-coordinate of this top side, we can multiply the lengths of the sides <math>a_1</math> <cmath>y\textrm{-coordinate} = \sum_{k = 1}^{\frac{n}{2}}a_k \cdot \sin \frac{2\pi(k-1)}{n}.\textbf{ (14 KB (836 words) - 16:58, 7 December 2022