Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [plane-geometry]

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded in a 2D plane.

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded in a 2D plane.

1925 questions
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The longer the base, the longer the hypotenuse

Excuse me if this is a silly question, but my plane geometry is very rusty. When I re-read Jack D'Aurizio's answer to the question "How can we prove that $\pi > 3$ using this definition", I wondered why, when viewed from the perspective of high…
user1551
  • 139,064
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Points on the plane transformation

There are n points located arbitrarily on the plane. Let us perform the following transformation: every point 'jumps' to the nearest one. 'A jumps to B' means that the point A coordinates after the transformation are equal to the coordinates of the…
Ego
  • 53
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3 answers

Calculate the height (z-coordinate) of a point on a flat quadrilateral plane

I'm not sure how to calculate the height of a point on a plane. Plane {ABCD}, shown from above, with point E within the plane: : : ··A----------B·· | | | E | | | | | ··D----------C·· : …
optimus_subprime
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1 answer

Maximum and minimum distance of two points

Consider six distinct points in a plane. Let $m$ and $M$ denote respectively the minimum and the maximum distance between any pair of points. Show that $M/m \geqslant \sqrt{3}$.
Sourasekhar Banerjee
  • 107
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What is the relationship between the length of the circumradius and the inradius in $ \triangle ABC $?

For reference: In a right angle triangle ABC, an interior bisector BD is traced, where I is or incenter, $\measuredangle B = 90 ^ o$ and $3BI = 4ID$. Find the relationship between the circumraio and inraio lenght of $\triangle ABC$. (Answer:3) My…
peta arantes
  • 6,211
3
votes
3 answers

Figuring out shape of four points scattered in a plane(Quadrilateral)

Suppose you're given coordinates of four points $x_1,x_2,x_3,x_4$ , given the fact that the points lie in a plane and polygon is convex. Figure out the shape formed by these four. So, in a 'brute force' way I have two methods. One is sketching the…
tryst with freedom
  • 11,538
2
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Extrinsic curvature of a 2-d plane

Imagine there is a 2-d plane as in Fig 1. I know nobody can live on a 2-d plane, but imagine a Flatlander standing (if that's what Flatlanders do) at position A. The Flatlander can then move through position B to position C. If we then give the…
JeffR
  • 121
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1 answer

What's the measure of $\angle x$ in thefigure below?

For reference: Calculate $x~ if AE = BC, and AD = BE$ My progress: I tried for auxiliary lines...parallel to BC by A and parallel to BE by A... forming the parallelograms...I completed the Angles but I was unsuccessful...but I believe the solution…
peta arantes
  • 6,211
2
votes
1 answer

Is a plane $z=x+y$ a function?

Can we think of plane in three-dimensional space as a function of 2 variables? In other words, is the plane $z=f(x,y)=x+y$ a function?
ssane
  • 443
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2 answers

Rational distance problem

My question is related to kind of problems, called "rational distances problem"(at least by wolfram mathworld). I couldn't find a specific solution, so it would be a real help if you have an idea or link about the solution. Here is the problem…
Cna Mrz
  • 234
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How can I prove the betweenness of the tree straight segments

I come across an elementary geometry problem as following: Assume that $\angle CAD=12°, \angle CBD=24°, \angle CAB=36°, \angle ABD=48°.$ Estimate that $\angle ACD=?$ And I tried so far: Construct along the straight segment $AC$ an equilateral…
azc
  • 1,259
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Finding the equation of a plane

Three planes have the equation $$ \pi_1:x+2y-3z=-4$$ $$ \pi_2:2x+y-4z=3$$ $$ \pi_3:x+2y-3z+4+\lambda(2x+y-4z-3)=0$$ Find the equation of the plane $\pi_3$ which passes through the line on which $\pi_1$ and $\pi_2$ meet and contains the point whose…
mathnoob123
  • 1,373
2
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2 answers

Tangent plane of a surface (an ellipsoid?) parallel to another plane

I need to find the tangent plane of $x^2+2y^2+3z^2=21$ that is parallel to $x+4y+6z=0$. Since our current topic covers parametrisations I was wondering if there is a good way to describe the curve in question as $\vec r(t)$. Both paths to the…
Katpton Liamfuppinshire
  • 317
2
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finitely many lines in a plane

There are finitely many lines in a plane $\mathbb{R}^2$. $\textbf{None of them is parallel}$. For each line $L$ which intersects with other lines say at $A_1$, $A_2$, $\cdots$ , $A_n$ in the consecutive order, it is called (1) well-divided (w.d.) if…
Haoran Chen
  • 21
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prove that the bisector of any angle exist and is unique.

This question from college geometry-discovery approach written by Kay, David C. I don't know how can I prove that question. Could you help me please?
Nunal
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