shape, congruence, similarity, transformations, properties of classes of figures, points, lines, angles
0
votes
0answers
3 views
Placing two mean proportions between two lengths
Lets have the right angle triangle ABC, and D, F two points on the hypotinuse AC. What are the necessary conditions to obtain the following ratios?
...
3
votes
1answer
27 views
Is there a temporal analogue of the four colour map theorem?
What is the minimum number of colours needed to prevent the same one being used, not just once in adjacent blocks, but also in consecutive time points? I understand the answer for 3d is infinite, but ...
0
votes
1answer
36 views
Griffths buffons needle
I've seen a lot of other proofs online about buffons needle, and I understand how they work, but I'm very confused about how Griffiths did this.
I just can't visualize it.
Needle Length L on ...
2
votes
2answers
33 views
Proof on an equilateral triangle with a cevian extended to its circumcircle
Consider the following figure with equilateral triangle $ABC$ and a cevian $AQ$ extended to $P$ on its circumcircle.
We are required to prove that:
$\frac{1}{PB} + \frac{1}{PC} = \frac{1}{PQ}$
...
-1
votes
1answer
28 views
Trianlgle homework [on hold]
The triangle formed by $$A(-2,-3) ,~~ B(1,3),~~ C(10,k)$$ is right-angled triangle at $A$, find:
a) the value of $k$,
b) the area of triangle $ABC$,
c) The length of $AM$ where $M$ is the mid-point ...
0
votes
2answers
28 views
How many whole bricks 6 × 12 × 24 cm3 will be sufficient to construct a solid cube of minimum size
How many whole bricks 6 × 12 × 24 cm3 will be sufficient to construct a solid cube of minimum size
I dont know how to tackle this minimum size condition . Can someone explain this part and solve the ...
0
votes
0answers
16 views
A problem on triangle and it's perpendicular bisectors.
I'm trying to solve the following problem :
"In △ABC, coordinates of $B$ are $(−3, 3)$. Equation of the perpendicular bisector
of side $AB$ is $2x + y − 7 = 0$. Equation of the perpendicular ...
0
votes
0answers
43 views
perimeter of a triangle. [on hold]
There is a triangle with a line down the middle of 4. Two bases of 4 and 3. A side of 5. And another side of 4 times the square root of 2. What is the perimeter? Id like to see your steps for future ...
1
vote
1answer
29 views
Optimal Configuration for a Set of Points
Consider a set of $n$ points on the plane with positions $\mathbf{p}_1,\dots,\mathbf{p}_n$, such that each point $i$ has at least one neighbor $j$ at a distance of no more than $\lambda$ away from it ...
1
vote
1answer
19 views
How to properly sort a set of axis-aligned boxes so they are drawn correctly under this projection?
Given a set S of axis-aligned, non-overlapping boxes {x,y,z,w,h,l}, where x,y,z are their center-positions and w,h,l their width, height and lengths, and given the following orthographic projection:
...
2
votes
1answer
141 views
The unsolved mathematical light beam problem
I have the following problem:
Imagine that you have a sphere sitting at the interface of two media(like water and oil). And the position(the heigth) of the interface to the center of the sphere is ...
4
votes
5answers
107 views
Pseudo code for calculating $\pi$ using an iterating algorithm?
So my question title says it all. What is the best way to calculate $\pi$ as an iterating algorithm that can be programmed into any application (thus the pseudo code)?
$\pi$ Was first calculated ...
5
votes
2answers
119 views
Can parallel lines meet? [duplicate]
Can parallel lines meet?
There is a person that takes a calculus course with us, and every time we ask him for something he answers us with I'll do it when two parallel lines meet each other. So I ...
5
votes
3answers
111 views
Geometry and Physics
I have to do a presentation on Geometry and Physics. I am asking it here (rather than physics.se) because I have to focus on Geometry More than Physics.
The intended audience is Undergraduate Seniors ...
2
votes
2answers
37 views
Are there exist $a, b >0$ such that $az_1^Tz_1 \geq b|z_1^Tz_2|$ and $bz_2^Tz_2 \geq a|z_2^Tz_1|$?
I am looking whether these inequalities can be held at the same time
$$az_1^Tz_1 \geq b|z_1^Tz_2| \\ bz_2^Tz_2 \geq a|z_2^Tz_1|,$$
where $a$ and $b$ are two positive constants, $z_i \in \mathbb{R}^2, ...
