I came up with the following question while playing around with Geogebra, and rather than do it myself I figured I’d offer it here. For a given ellipse, the director circle is defined to be the set of all points where two perpendicular tangents to the ellipse cross each other. Suppose we instead consider the […]

Why are the coefficients of the equation of a plane the normal vector of a plane? I borrowed the below picture from Pauls Online Calculus 3 notes: http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfPlanes.aspx And I think the explanation he provides is great, however, I don’t understand how one of the concepts work. If the equation of a plane is $ax+by+cz=d$ […]

A popular introductory description of a “tangent (in geometry)” is presented as “the tangent line (or simply tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point.“ I like to find out whether and how this description might be expressed or translated in the […]

Let $c_1,c_2,c_3$ be three circles of unit radius touching each other externally. The common tangent to each pair of circles are drawn (and extended so that they intersect) and let the triangle formed by the common tangents be $\Delta ABC$. Find the length of each side of $\Delta ABC$. I don’t have a clue how […]

This question from earlier today asks (paraphrasing here): Is there a configuration of $7$ points in the Euclidean plane such that, given any $3$ of the $7$ points, at least $2$ of them are $1$ unit apart? One such configuration, given in this answer, is the set of blue points in this diagram; the red […]

I found a conjecture: A chain of six circles associated with six points on a circle (in Mobius plane). This is a generalization of the last my previous question in Three chains of six circles. (Noting that, in this configuration: $P’_1P_1P_4P’_4$ don’t lie on a circle) I am looking for a proof of the conjecture […]

Is there a set of seven points in the plane such that, among any three of these points, there are two, $P, R$, which are distance $1$ apart?

The normals at three points $P$, $Q$, $R$ on a rectangular hyperbola $xy = c^2$ intersect at a point on the curve. Prove that the centre of the hyperbola is the centroid of the triangle $PQR$. I copied the the question word by word. Let assume that the points are (c$ t_1$,$\frac{c}{ t_1}$) , (c$ […]

Trisect sides of a quadrilateral and connect the points to have nine quadrilaterals, as can be seen in the figure. Prove that the middle quadrilateral area is one ninth of the whole area.

Intereting Posts

Comparing Hilbert spaces and Banach spaces.
Question on differentiability of a continuous function
Classifying complex $2\times 2$ matrices up to similarity
What is wrong with my integral? $\sin^5 x\cos^3 x$
A geometry problem (how to find angle x)
Simplifying an Arctan equation
How to prove $f(\bigcap_{\alpha \in A}U_{\alpha}) \subseteq \bigcap_{\alpha \in A}f(U_{\alpha})$?
Limit involving $(\sin x) /x -\cos x $ and $(e^{2x}-1)/(2x)$, without l'Hôpital
Viewing forcing as a result about countable transitive models
When does function composition commute?
Question on computing direct limits
Is it possible to find $n-1$ consecutive composite integers
Is an irreducible element still irreducible under localization?
Classifying groups of order 90.
How to count derangements?