# Questions tagged [geometry]

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.

33,808 questions
Filter by
Sorted by
Tagged with
2answers
30 views

### A plane region of area $A$ is inclined at an angle $\theta$ to another plane. Why is the area of the region's projection in that plane $A \cos\theta$?

How come that $A_1=A_2 \cos(\theta)$?
3answers
33 views

### Visual Interpretation for the Sum of a Finite Geometric Series

I'm interested in intuitive visual explanations for the sum of a finite geometric series. I know there are some pretty "intuitive" explanations out there (including some on this site), but I haven't ...
1answer
42 views

### Failing to visualise Steiner's argument - Isoperimetric Theorem

My question is regarding Steiner's (incomplete) proof for the Isoperimetric problem, as presented in the book What is Mathematics. In a critical step, Steiner asks to readjust half the 'assumed' ...
1answer
28 views

### inequality for lengths of projections inside a circle

In the following picture, how can show that $c \leq a + b$? In the picture, $x$, $y$ and $z$ are three vectors of equal length. We can split $x$ in a component parallel to $y$ and a component ...
0answers
22 views

### Points on two perpendicular lines [on hold]

I got in troubles. I have no idea how to work with 3D lines, just with 2D lines. My problem is this: I got a point on a line and a point on a perpendicular line in 3D space. I have to get the gradient ...
0answers
34 views

### For non-negative $a$ and $b$ with $a+b \leq c$ for a small constant $c$, what is the minimum of $\cos a + \cos b$?

Let $a,b \geq 0$ with $a+b \leq c$ for a small constant $c$ between $0$ and $1$. What is the minimum of $\cos(a) + \cos(b)$? I conjecture it is $\cos(0)+\cos(c) = 1 + \cos(c)$ but I have no ...
5answers
39 views

### The horizontal side length of one of four small rectangle is a and the vertical side length is b. Verification: a + b = 1.

A square ABCD with a side length of 1 is divided into five small rectangles, four of which have the same area. The horizontal side length of one of four small rectangle is a and the vertical side ...
4answers
51 views

### Square with midpoints of $AD$ and $CD$

Square $ABCD$ is given; $MA=MD=ND=NC$. Show $AF=AB$. The first thing I noticed was $\triangle CDM \cong \triangle BCN$ and we obtain $CM = BN$ and $\angle MCD = \angle NBC$. Now I am trying to ...
2answers
21 views

### Finding the points that line on a plane

Let $P$ denote the plane given by the point-normal equation: $0 = (1,2,−1)·((x,y,z)−(1,1,1))$ How do I find the points $(x, y, z)$ that lie on the plane $P$?
0answers
61 views

### Compute face angles for a snub disphenoid (Johnson solid J84)

What I understand so far: This shape has 12 triangular faces (all equilateral triangles since this is a Johnson solid) and 8 vertices. We have 4 faces meeting at 4 of the vertices and 5 faces meeting ...
0answers
26 views

### Geometry of Envelope form definition

I had read about the envelope of the family of the curve. It is defined as a curve which is tangent to each member of the family at a single point and it is union of all such points. To find envelope ...
0answers
16 views

### Prove that orthocenter of an orthic triangle is the bigger triangles circumcenter [on hold]

I have tried to prove this fact for some time now.I tried angle chasing, looking at cyclic quadrilaterals and looking for similar triangles but none of it is taking.
2answers
70 views

4answers
73 views

### Angles between vectors of center of two incircles

I have two two incircle between rectangle and two quadrilateral circlein. It's possible to determine exact value of $\phi,$ angles between vectors of center of two circles.
1answer
28 views

### Application of hyperspheres [on hold]

Recently I've been studying the the volume of an n-ball. Do hyperspheres (or their volume/surface formulas) have any real-world applications?
1answer
28 views

0answers
21 views

### Is it possible to make a stereographic projection of a stereographic projection?

Since we can't visualize a 3-sphere directily, I was wondering how does its stereographic projection look like, and found this neat demonstration: https://demonstrations.wolfram.com/...
0answers
17 views

### Divide circle and subcircle evenly by area

How do you divide a circle into a certain number of shapes with the same area while having at least one sub circle dividing the whole figure? I know that if we divide along the center of the circle in ...
2answers
27 views

### Calculating the coordinates of a unit vector normal

First of all I apologize if the question is elementary, I have not practiced math for a long time and have only just slowly picked up the fundamentals again. (i) With reference to Figure Q4, ...
0answers
27 views

### Elliptic element points of order 2 and 3 in the Fundamental Region for $PSL(2,\mathbb{Z})$

I am aware the Fundamental region for $PSL(2,\mathbb{Z})$ has 3 vertices, namely: $\rho = \frac{-1+i\sqrt{3}}{2}$, $\rho +1 = \frac{1+i\sqrt{3}}{2}$ and $i$, each stabilised by the cyclic subgroups ...
4answers
3k views

### Trying to visualize the hierarchy of mathematical spaces

I was inspired by this flowchart of mathematical sets and wanted to try and visualize it, since I internalize math best in that way. This is what I've come up with so far: Version 1 (old diagram) ...
2answers
45 views

### Flat geometry(what would the drawing of this figure look like?including the values)

Consider a right-angled triangle and the circumference inscribed on it. The point of contact between the hypotenuse and the circumference determines in the hypotenuse segments 4meters and 6meters, ...
1answer
33 views

1answer
71 views