Questions tagged [analytic-geometry]
Questions on the use of algebraic techniques for proving geometric facts. Analytic Geometry is a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles being the most basic of these. It is concerned with defining and representing geometrical shapes in a numerical way.
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Perpendiculars passing through diagonal intersection in a quadrilateral formed within a square
Let $ABCD$ be a square with points $F \in BC$ and $H \in CD$ such that $BF = 2FC$ and $DH = 2HC$.
Construct:
Line through $F$ parallel to $AB,ドル meeting $AD$ at $E$
Line through $H$ parallel to $BC,ドル ...
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Proof of the wheel stud problem
Consider a regular $n$-sided polygon in two-dimensional space (metaphorically: the stud pattern on a typical car wheel), and a sequence to choose each of its sides exactly once. If the choice sequence ...
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Are analytifications in Berkovich geometry strict k-analytic spaces?
Let $k$ be a non-archimedean complete field. Berkovich defines the analytification of a $k$-schemes $X$ which are locally of finite type via the assignment
$\mathrm{Spec}(A) \mapsto \mathcal{M}\mathrm{...
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Find the ratio of $BA:AC:CB$ if a certain point $D$ on triangle $\triangle ABC$ satisfies a ratio
Let $D$ lie on side $AB$ of right-triangle $\triangle ABC$ such that $AD:CD:DB = 3:2:1$
Then, find the value of $BA:AC:CB$
The only method I could think of would be to use coordinates where $C=(0,0), ...
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Finding the points on a cone where the tangent plane contains the line formed by intersecting two given planes
There are several resources (especially Calculus books) that talk about finding tangent planes to a given (level surface) with certain prescribed conditions. I was trying to make a general question ...
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what does analytically isomorphic mean for complex spaces?
Here"analytically isomorphic"means that the completion of the local rings of two points in some complex spaces are isomorphic. The smooth case is trivial so the only interesting case is that ...
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Maximum area shape that can pass through concatenation of constant curvature channels
Which shape fits inside and can completely pass through a channel defined by a two dimensional curve with thickness $t$ (its walls are at distance $±t/2$ from the centerline) and consisting of a ...
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What is the correct definition of "double tangent"?
In the literature , there are two definitions of "double tangent".
One of these is a single straight line which is tangent to a curve at two different points.
I am not worried about this -- ...