Tagged Questions
3
votes
1answer
114 views
Cutting a cube by plane cuts
This is an extension of a 3rd grade problem.
How many pieces can one get at most if one cut a unit cube with n plane cuts?
1,2,4,8, ???
And assuming cutting through an area 1 takes time t, what is ...
4
votes
1answer
93 views
Trisecting a paper using hand and without using a ruler or compass
This is a practical problem born while folding a paper.
We can bisect a paper by using only hand.
$\star$ Easy, fold it so that the two ends (of the length) coincide and press
the paper to get ...
0
votes
0answers
46 views
What's the difference between a 2-sided and 2-sided strip polytan
There are 14 2-sided tetratans and 13 2-sided strip tetratans. The sets are identical, except the square is missing in the strip version. My best guess is that for strips, no vertex can have an edge ...
58
votes
4answers
1k views
Probability that a stick randomly broken in five places can form a tetrahedron
Randomly break a stick in five places.
Question: What is the probability that the resulting six pieces can form a tetrahedron?
Clearly satisfying the triangle inequality on each face is a necessary ...
0
votes
1answer
29 views
Dividing an arbitrary $2-D$ shape with integer area into arbitrary shapes of unit area
The name explains it all. I searched for it in MSE and came across a similar [one] but more simpler1. I was interested to know if we can prove that, i.e., given an arbitrary shape (closed and ...
0
votes
3answers
110 views
Intersection of chord with circle knowing the length and a point
Let's take a circle with radius R, and center in O (0, 0). We take on this circle a point A with coordinates xA and yA.
We know that point A is one of the endings of a chord with length l.
Which is ...
3
votes
1answer
112 views
Triangle from a given rectangle
We are given a set of (marked) points in a 2D coordinate system and function $f(x,y)$ which counts number of points marked in the rectangle $(0 , 0), (x , y)$ - where $(0 , 0)$ if down-left corner, ...
4
votes
2answers
135 views
How to Construct orthogonal circles?
Let $C_{1}$ be a circle of unit radius. Let A and B be two points inside $C_{1}$. Now I want to construct another circle $C_{2}$ such that A and B lie on $C_{2}$ and $C_{2}$ is orthogonal to $C_{1}$ ...
1
vote
1answer
134 views
Dissection of a chess board into 4 congruent pieces
Consider a standard $8\times 8$ chessboard where a pawn is placed on each of the squares $d1,d2,d3,d4$ . Dissect the board into $4$ congruent pieces (reflections are allowed) such that each piece ...
1
vote
2answers
97 views
Is my proof that the medians of a triangle are concurrent valid?
Consider any triangle ABC. Connect the midpoints of each of the three sides. The inscribed triangle is equal to the other three triangles and they are all congruent. It turns out that the medians of ...
0
votes
1answer
50 views
Closest Packing of Spherical Caps
Let the surface $S_n$ of the unit ball in $\mathbb{R}^n$ centered at the origin $O$ be defined as the set of points $P(x_1,x_2,…,x_n )$ such that $x_1^2+x_2^2+⋯+x_n^2=1$. Let the spherical cap $C(α)$ ...
1
vote
1answer
218 views
Puzzle on the triangle.
In triangle top four figures that have to be repositioned to form the "triangle" without a unit square.
How to explain this?
Thank's.
0
votes
2answers
220 views
What is the significance of the mirror numbers?
I'd like to hear insights and theory of the mirror numbers and their possible significance in mathematics and geometry. With mirror numbers I mean these four examples:
...
11
votes
1answer
215 views
What hexahedra have faces with areas of exactly 1, 2, 3, 4, 5, and 6 units?
I tried for a while, not very hard, to construct a polyhedron with exactly six faces, whose areas were respectively 1, 2, 3, 4, 5, and 6 units. I did not meet with any success. Still, it seems that ...
4
votes
0answers
142 views
“Green Globs” question
When I was in high school geometry, we had a fun little game on the computer called Green Globs (the website for the software is http://www.greenglobs.net/index.html). A number of targets (globs) are ...
1
vote
0answers
59 views
Zome construction
I'm preparing a presentation on Penrose tiles, and I want to talk about how we can get non-periodic tilings of the plane by taking projections of slices of higher-dimensional periodic tilings (in ...
21
votes
3answers
904 views
Guaranteed Checkmate with Rooks in High-Dimensional Chess
Given an infinite (in all directions), $n$-dimensional chess board $\mathbb{Z^n}$, and a black king. What is the minimum number of white rooks necessary that can guarantee a checkmate in a finite ...
6
votes
3answers
244 views
Puzzle: A coin rolls without slipping around another coin
If a coin rolls without slipping around another coin of the same or
different size, how many times will it rotate while making one
revolution?
The proof given is like this:
Cut the curve ...
5
votes
1answer
199 views
A cute geometry problem about angle trisectors.
Here is a cute geometry problem I saw some time ago. I know the solution, I just wanted to share ;-) (Please, don't be mad at me.)
Consider an acute triangle $\triangle ABC$. Let $AP$, $AQ$ and ...
1
vote
2answers
699 views
Chords on a Circle
If there are N points on a circle, and you draw a chord between each
of them, how many regions is the circle subdivided into?
I'm not quite sure where to begin. I know that there are at least n ...
25
votes
1answer
834 views
Dividing a square into equal-area rectangles
How many ways are there to tile an $n\times n$ square with exactly $n$ rectangles, each of which has integer sides and area $n$?
The sequence $C(n)$ begins 1, 2, 2, 9, 2, 46, 2, 250, 37. Clearly ...
3
votes
2answers
111 views
How to mathematically color the regions bounded by a parametric curve?
Usually, if an implicit equation F(x,y) = 0 defines a curve (or curves) on the x-y plane, then we can use the inequalities F(x,y) < 0 or F(x,y) > 0 to color the regions bounded by the curve (or ...
4
votes
2answers
138 views
The area problem!
We have to find area of the quadrilateral formed by joining the point of intersection of the four quarter circles that are drawn from each vertex in a unit square.
$\hspace{4cm}$
The challenge is ...
0
votes
3answers
299 views
Tiling with polyominos
How to prove or disprove that if a polyomino tiles the plane, it must also be able to perfectly tile some larger polyomino, which also tiles the plane?
A polyomino is finite set of unit squares ...
1
vote
2answers
185 views
Find the angle between two lines using a compass and straight edge.
I've drawn two random, non-parallel, straight lines on a plane. They cross over, forming two angles, a and b, where (a + b + a + b) = 1 (or 360°) and a ≤ b. (Making a either the acute angle or a right ...
4
votes
0answers
137 views
Which chapters of Euclid's elements would be helpful for drawing a grid?
I am drawing a $19 \times 19$ grid on my desk. For aesthetic purposes, I don't want to use a ruler. Rather, I want to use Euclidean theorems to 'prove' to myself that such and such line meets at a ...
3
votes
1answer
163 views
Decomposing a circle into similar pieces
Is it possible to decompose a circle into finitely many similar disjoint pieces, one of which contains the circle's center in its interior?
13
votes
2answers
389 views
The Farmyard problem
Problem:
There is a farmer who has a $1\text{ mile}\times 1\text{ mile}$ square piece of land. He knows that there is a completely straight pipe underneath some part of his property, but it could ...
-1
votes
3answers
319 views
Triangle whose height and sides are consecutive integers
This is probably a old puzzle,and maybe you have seen it somewhere else before.Imagine a special triangle. The height and the three sides of this triangle are 4 consecutive integers.Can you figure out ...
3
votes
1answer
83 views
Eight queens problem, wondering about the non-unique solutions
I've done the code that generates all the solutions. But know I am suppose to filter out any redundant solutions based on symmetry and rotations. I have code for vertical symmetry, horizontal ...
9
votes
4answers
858 views
Ten soldiers puzzle
This is a puzzle from one popular book called "The Man Who Counted: A Collection of Mathematical Adventures",author is Malba Tahan. How to arrange ten soldiers in five lines in such a way
that each ...
3
votes
0answers
302 views
Space-filling polyhedra (or honeycomb) survey?
Is there a survey anywhere of space-filling polyhedra? MathWorld's article, space-filling polyhedron, mentions about 400 being seen in pre-1981 books and papers. Wikipedia mentions 28 convex uniform ...
70
votes
3answers
3k views
What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?
What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?
The image below is a flawed example, from http://www.mathpuzzle.com/flawed456075.gif
...
2
votes
4answers
759 views
Why does rearranging the pieces of this triangle illusion give a different area? [duplicate]
Possible Duplicate:
How come 32.5 = 31.5?
4
votes
1answer
455 views
Interesting Taxicab Problem?
I came up with this problem after discussion of taxicab geometry in math class... I thought it was a simple problem, but still pretty neat; however, I am as of yet unsure of whether my answer is ...
34
votes
6answers
3k views
