https://math.codidact.com/categories/41/tags/3949.rssNew Posts Tagged 'geometry' - MathematicsMathematics - Codidact2024-03-20T14:20:43Zhttps://math.codidact.com/posts/291104Find length $MP$ in trapezoidTheCodidacter, or rather ACodidacterhttps://math.codidact.com/users/609342024-03-20T11:15:58Z2024-03-20T14:20:43Z<p>Trapezoid $ABCD$ is given such that $AB\parallel CD$ and $AD=BD$. Let $M$ be the midpoint of $AB$ and $P$ be the intersection of diagonal $AC$ with the circumcircle of $\triangle BCD$. Given tha...https://math.codidact.com/posts/288409Average distance from circle's center to a pointTheCodidacter, or rather ACodidacterhttps://math.codidact.com/users/609342023-06-14T07:24:44Z2023-06-15T07:13:50Z<blockquote>
<p>What is the average distance from a point inside a circle to the circle's center?</p>
</blockquote>
<p>I came across this problem, and I've heard the solution is $\frac23R$ for t...https://math.codidact.com/posts/287562Dividing a cuboid in fourYair Randhttps://math.codidact.com/users/531262022-12-16T03:02:31Z2022-12-19T15:26:15Z<p>Suppose we have an irregular cuboid (that is, a hexahedron with six irregular quadrilateral faces) ABCDEFGH that we wish to divide into four smaller cuboids, such that three of them each fully s...https://math.codidact.com/posts/287174How to calculate remaining volume of a wire spoolre89jhttps://math.codidact.com/users/553482022-10-06T23:52:49Z2022-10-07T12:40:13Z<p>There are a bunch of rolls of 3d filament at my library in various degrees of emptiness/fullness. When I pick one I need to know that it likely has enough remaining for my print job.</p>
<p>Ho...https://math.codidact.com/posts/286140Finding distance to parabola's focus, given some pointsmsh210https://math.codidact.com/users/81062022-03-21T20:44:16Z2022-10-03T08:24:52Z<p>A high school student I know has the following problem:</p>
<blockquote>
<p>A parabola is given by $y^2=2px$ with $p>0$. The point $D$ is on the parabola in the first quadrant at a distance...https://math.codidact.com/posts/285671How can you "easily see that such squares [of side length $\sqrt{13}$ and $\sqrt{18}$] will not fit into the [4 × 4] grid"?DNBhttps://math.codidact.com/users/536282022-01-24T03:45:23Z2022-01-28T12:29:42Z<blockquote>
<p>Problem 2.4: How many squares of any size can be formed by connecting dots in the grid shown in Figure 2.2.</p>
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<p>I skip p 31, but apprise me if you want me to inc...https://math.codidact.com/posts/284996How do mathematicians measure area for points?deleted user#2021-11-27T06:59:36Z2021-12-20T10:04:42Z<p>There are two points (adjacent or not adjacent) on top of an infinite plane; how to measure how much area they catch together, as a "set".</p>
<p>Because that if we put a minimal border around ...https://math.codidact.com/posts/285052What is the parallel for edges?deleted user#2021-12-02T12:38:07Z2021-12-03T08:31:16Z<p>What is the parallel to <a href="https://en.wikipedia.org/wiki/Edge_(geometry)">edge</a> in curves?</p>
<p>For example, if we have three points and three edges we get a triangle but if we defin...https://math.codidact.com/posts/283281How do mathematicians measure shape perimeters?deleted user#2021-08-10T22:40:47Z2021-08-13T00:58:39Z<p>When I create a circle on a computerized plane with a graphic editing program (such as Window's Paint), I can see a group of dots circling around an imagined central point.</p>
<p>if the perime...https://math.codidact.com/posts/282013Why do 3D mental pictures usually suffice for high-dimensional geometry?Chgg Clouhttps://math.codidact.com/users/535642021-06-04T04:32:18Z2021-06-04T04:32:32Z<p>Kindly see the embolded phrases below. The author doesn't expound why the 3D "mental pictures" are "usually enough". Scilicet, why doesn't "this impoverished vision"...https://math.codidact.com/posts/282012How can you foretell if a problem is one whose solution admits a simple mathematical description?Chgg Clouhttps://math.codidact.com/users/535642021-06-04T04:31:47Z2021-06-04T04:31:47Z<p>Kindly see the emboldened phrase below. What kind of problems is the author referring to?</p>
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<h3>THE UNREASONABLE EFFECTIVENESS OF CLASSICAL GEOMETRY</h3>
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<blockq...https://math.codidact.com/posts/280842Does every divergence-free vector field arise as the curl of some vector field?The Amplitwisthttps://math.codidact.com/users/535162021-02-17T18:51:20Z2021-02-20T19:38:13Z<p>I was introduced to the concepts of gradient $\nabla f$, curl $\nabla \times F$ and divergence $\nabla \cdot F$ in an introductory course on calculus during my undergraduate studies. There I lea...https://math.codidact.com/posts/278332Cutting the squareGrovehttps://math.codidact.com/users/534522020-10-01T21:53:10Z2021-01-18T15:15:15Z<p>I don't know how simple/diffcult this is, but it has been on my mind for some time, and I haven't managed to do anything about it, so now I'll try here to see if anyone has any input.</p>
<p>Le...https://math.codidact.com/posts/280460What surface do I get by attaching $g$ handles as well as $k$ crosscaps to a sphere?The Amplitwisthttps://math.codidact.com/users/535162021-01-13T18:25:39Z2021-01-13T19:09:42Z<p>I recently found out that there is a classification of compact connected surfaces that says that every such surface (or, $2$-manifold) is homeomorphic to either $S_g$, the sphere with $g \geq 0$...https://math.codidact.com/posts/280204Given a triangle with squares on two sides, the line segments joining the centres of the squares to the midpoint of the third side are equal and perpendicularThe Amplitwisthttps://math.codidact.com/users/535162020-12-31T02:06:40Z2021-01-03T14:41:34Z<p>I am reading Tristan Needham's <em>Visual Complex Analysis</em> (2012 reprint, OUP), and in $\S$1.III.3: <em>Geometry</em>, the author gives a geometric proof of the following fact, shown in Fig...https://math.codidact.com/posts/278647Method to calculate the area of a cyclic n-gonRazetimehttps://math.codidact.com/users/533102020-10-20T08:40:27Z2020-10-20T09:15:01Z<p>The area of a cyclic quadriateral, given the side lengths, is given as follows:
$$
\sqrt{(s-a)(s-b)(s-c)(s-d)}
$$</p>
<p>(Brahmagupta's formula)</p>
<p>Where $
s = \frac{a+b+c+d}{2}.
$</p>
<p>I ...