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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When do a triangle and its Morely triangle have the same centroid

When do a triangle and its Morley triangle have the same centroid? For definition of the Morley Triangle see https://en.m.wikipedia.org/wiki/Morley's_trisector_theorem#Morley.27s_triangles
Ali Taghavi
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How many unit paths in $\mathbb R^3$ of length $9$ starting from the origin?

I have a general formula for the number of unit paths to be $a+b+c \choose a$ (which I'm not even certain is correct). I know $a+b+c=9$ but how do you determine what the bottom should be? I believe the answer should be a summation but am not sure of…
Alex
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How many unit paths are there in R3

How many unit paths are there in $\Bbb R^3$ from $(0,0,0)$ to $(n,n,n)$ that never pass below the plane $y=x$? This means that for every point $(a,b,c)$ on the path we have $a\le b$.
KGT
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Finding An Isosceles Triangle

Can we always find an isosceles triangle of the same area as the original scalene triangle? If so, could you please provide a compass straight edge proof?
Jyotishraj Thoudam
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Plane equation exercise

.Find the plane equation that contains the X axis and the point A(4,-3,-1) The correct answer is y-3z=0 Anyone could explain me why is that the answer and is not -3y-1z=0? Thanks you in advanced! Sorry for my English, I'm Spanish
Ceci
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Plane geometry and straight lines

I am trying to understand a statement of a problem. Wondering how can a striaght lines in three different planes meeting at one point. Does not it imply that all the three planes are also intersecting at some line?. Can three lines in parallel…
Avaneendra Alugupalli
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We can assign a colour, red or blue, to the points of a plane so that there isn't a segment of same colour

Prove we can assign a colour, red or blue, to the points of a plane so that there isn't a segment of same colour.
user261263
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equiangular triangle and law of cosine

How can I prove that Equiangular triangles are equilateral in plane geometry using Law of cosine? How is it that equiangular triangles are equilateral is a direct consequence of law of cosine?
Jyotishraj Thoudam
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Why are the diagonals of a parallelogram not equal?

Imagine a parallelogram and draw its diagonals. Now the areas of the two triangles on one of the bases is equal. But by Heron's formula, the areas are not equal. So what is the explanation for it.
urkarsh jain
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Show that $r=\langle x,y\rangle$ satisfies $(r-a)\cdot (r-b)$ iff $(x,y)$ is on a circle

Given that $a=\langle a_1,a_2\rangle$, $b=\langle b_1,b_2\rangle$. How can we show that $r=\langle x,y\rangle$ satisfies $(r-a)\cdot (r-b)=0$ iff $(x,y)$ is on a circle? What would be the center and radius of such a circle in terms of vector…
Tori Small
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Intersection of planes and calculating the equations

Two planes: 4a - 6b + 8c = 3 -9a + 12b -3c = -10 What steps are there to calculate the equation of the line when the planes intersect?
JimboZone
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which statement is true and why?

Let A and B be two distinct points in the plane, d their distance apart, and r a given positive integer. Then (A) there always exists a circle of radius r passing through A and B (B) if d ≤ 2r then there exists a unique circle of radius r passing…
acemi123
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circumcenter coincides with center of mass

I am trying to prove the following statement. Any suggestions or references are highly appreciated. Consider $n$ points in $R^2$, i.e., $x_i\in R^2, i=1,\ldots, n.$ Suppose the centroid (or center of mass with unit mass) denoted as…
Chandler
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How to find disjoint set of two planes in form $ax+by+cz=d$?

How to find disjoint set of two planes in form $ax+by+cz=d$? How do I need to alter the equations?
mavavilj
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Proving two lines don't intersect

The line $l_1$ passes through the position vector $i-j-2k$ and is parallel to the vector $3i-4j-2k$. The line $l_2$ passes through the position vector $(1+5\cos t)i-(1+5\sin t )j-14k$ where $0≤ t≤2\pi$ and is parallel to the vector $15i+8j-3k$.…
mathnoob123
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