7
votes
2answers
70 views

Evenly space holes in circle

A picture is worth a thousand words: This gear is part of an interactive SVG Spirograph I'm creating. I'm dynamically generating the gear based on a number of parameters (gear radius, number of ...
-1
votes
1answer
92 views

What proportion of the circle is covered by the square?

Or what is the combined area of the circle segments (chords)? Picture a circle which is covered by a square, where the bottom vertices of the square are inscribed within the circle (so that the ...
0
votes
2answers
67 views

Questions about area

In math class (I'm in Geometry) I was messing around and decided to try and find the area of a circle using the area of a square if the radii are the same length. The square is inscribed in the ...
1
vote
2answers
43 views

The rate change of the radius of a coil.

Suppose I have a tube of radius $r_0$ that I want to wrap a sheet of length $l$ and thickness $\Delta x$. Assuming the radius changes only when the paper overlaps the where the previous section ...
1
vote
1answer
32 views

How fast will a shape grow if it can grow exponentially only at the border, and growth is limited by crowding?

Take a hypothetical bacterium which divide once per minute. After $n$ minutes there will be $2^n$ bacteria, assuming no constraints. But what if its growth is constrained by resources and space? I am ...
0
votes
1answer
19 views

How to Find the Remaining Length of a Cone With Only a Part of It

I took three measurements for a certain plastic cup in my kitchen. One was of the circle on the bottom of the cup, and the other was the top(the larger opening) and the height in between the two. ...
5
votes
0answers
83 views

Geometrical question just for fun

Was puzzling with the following (home made) puzzle: Given the square $ABCD$ with $A = (1,1)$, $B = (1,-1)$, $C = (-1,-1)$ and $D = (-1,1)$ And given point $E = (0,2)$ What is the smallest (by ...
0
votes
1answer
39 views

Solve Spherical Shell for Radius given Thickness and Volume

I'm looking to calculate the outer radius of a spherical shell of a desired volume and thickness. I don't know if the years have knocked some obvious obstacle out of my perception, but here's what ...
2
votes
2answers
61 views

Orthogonal tangents to an ellipse [duplicate]

This is the problem I found back in the first year in the university. Suppose we have a non-degenerate (i.e. not a point and not an empty set) ellipse $E\subset \Bbb R^2$. Now define a set $D$ by a ...
92
votes
10answers
11k views

How can a piece of A4 paper be folded in exactly three equal parts?

This is something that always annoys me when putting an A4 letter in a oblong envelope: one has to estimate where to put the creases when folding the letter. I normally start from the bottom and on ...
1
vote
1answer
75 views

Simple Circle Problem

An elegant circle problem. It goes by many names. This is my version. Dog 1 is tied to a post by a leash 1 unit long. He shares half of his land with Dog 2 tied to a post 1 unit away from his own. ...
7
votes
0answers
84 views

Knight's metric: ellipse and parabola.

Knight's metric is a metric on $\mathbb{Z}^2$ as the minimum number of moves a chess knight would take to travel from $x$ to $y\in\mathbb{Z}^2$. What does a parabola (or an ellipse) became with this ...
0
votes
3answers
894 views

How do you find the altitude in a pyramid? (SAT math question)

The pyramid shown above has altitude h and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m? A) ...
0
votes
1answer
395 views

How many triangle can be drawn with those points? [duplicate]

There are 7 points on the circumference of a circle.How many acute triangle can be drawn with those points. please help me to solve this problem.
0
votes
1answer
94 views

What is the meaning of $(x^2+y^2)^n$? Is this an already known geometric object?

We all know that $x^2+y^2=r^2$ is a circle. What does $(x^2+y^2)^2$ signify? In general, what is $(x^2+y^2)^n$?
0
votes
1answer
95 views

what is the most sided sturdy regular n-polygon that can be made with lego?

Was puzzeling with this question: What is the most sided regular n-polygon that can be made with lego? It has to be sturdy (the polygon should stay in shape when pushed around) made with the normal ...
1
vote
1answer
157 views

tangram cannot get a square with a little square hole in the center

From a tangram or seven-piece puzzle (first picture), we cannot get a square with a little hole in the center (the second cartoon), the hole is also a square Why?
0
votes
2answers
76 views

Solve for the angle of two straight lines on a 3 dimensional plane.

On a $3$ dimensional plane: Given that two vectors $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ are known and that each of these vectors belong to two separate straight lines ...
1
vote
1answer
101 views

Intersecting Circles Theorem (about 1983 AIME #14's solution)

Please consider this problem: http://www.artofproblemsolving.com/Wiki/index.php/1983_AIME_Problems/Problem_14 Now look at solution 2 - it assumes that A, B, and R are co-linear, but does not prove ...
4
votes
1answer
645 views

Can you make an equilateral triangle from 3identical trapezoids?

Is it possible to make an equilateral triangle from 3 identical trapezoids? If so, what angles would be needed in the trapezoids?
0
votes
0answers
30 views

Volume of remanining part of sphere? [duplicate]

Can some one explain the question? I didn't understand the question clearly.
4
votes
2answers
107 views

Number of cells inside a circle

Suppose we have a circle with diameter `r˙ whose center is in the center of a cell. I would like to calculate how many cells are inside this circle (even if only a fraction of the cell is inside). How ...
3
votes
1answer
376 views

Solving circle's radius only knowing angle & lengths of external triangle OR solving for sides of a triangle partial side lengths

Is this possible? Given that I know the length of Y and Z and the angle of X can I figure out the radius A? If I can't without more information, I can produce another set of data X Y Z at a ...
3
votes
3answers
397 views

Minimizing perimeter given rectangle's area for 10-years-olds

I was recently in touch with some person from Russia how is busy with books for Russian elementary schools, in particularly I learned that now they give elementary set theory for the 2nd grade ...
0
votes
0answers
79 views

Did I make a “forced” interpretation?

Just a few years ago I wrote an article called The Geometry of the MRB constant. Since then I've wondered if there is a better, more natural geometric analysis of the following summation. $$ ...
5
votes
2answers
917 views

Can you divide a square into 5 equal area regions

Given this shape: Is it possible to divide the cyan area into 5 equal area shapes such that: Each shape is the same Each shape has an edge touching the red square Each shape has an edge touching ...
0
votes
1answer
260 views

Among these figures circle, square, rectangle, isosceles triangle which has the greatest perimeter had the same area?

Among these figures circle, square, rectangle, isosceles triangle which has the greatest perimeter had the same area geometrically ?
1
vote
1answer
76 views

Radius ratio for four packed circles

Suppose we are given four circles $A,B,C,D$ in the Euclidean plane having radii $r_A,r_B,r_C,r_D$ such that $r_A=r_C,r_B=r_D$ and circles $A,C$ are tangent to each other and to $B,D$ but $B,D$ are ...
0
votes
1answer
62 views

Partition of circumference into $3k$ arcs

The following problem is from 1982 Russian Mathematical Olympiad. If you go to this link, and scroll down to the section Russian Math Olympiad, then this is Problem 333 in that text-file. Let $k$ ...
16
votes
1answer
644 views

Why are these geometric problems so hard?

I was surprised to learn that both for the Moving Sofa Problem and Packing 11 Squares solutions have been proposed, but in either case the optimality of the proposed solution is, as of yet, only ...
7
votes
2answers
227 views

What does it mean to be $0.9-$Dimension?

We can visualize $1\mathrm D$, $2\mathrm D$, $3\mathrm D$ and we can think of a higher $M-\mathrm {Dimension}$ where $M\in \mathbb N^+$as a vector. But I recently learned that there are non integer ...
2
votes
2answers
114 views

When does the triangle have the smallest area?

The following triangle has an area $S$, and the sides $AO$ and $BO$ have the length $a$ and $b$, respectively. There is a fixed point $X$ at $(x,y)$. A point $C$ is put on the line segment $OA$, and ...
1
vote
3answers
102 views

Finite number of points inside a disk

Let $n\ge 2$ and suppose that $z_1, z_2, \ldots, z_n$ are distinct points in the interior of some disk $D$ in the plane. Why is it true that there exists a smaller disk $D'\subseteq D$ such ...
1
vote
1answer
76 views

Confusing DE concept question

This is the question: A reduced copy of a painting by Kandinsky is placed on the top of original. Is there a point of the painting covered by a point of the copy which has the same color? If it is ...
7
votes
2answers
184 views

Question on triangle with heights

Prove that there exists no triangle with heights 4,7, and 10 units. I am completely puzzled.
3
votes
1answer
173 views

the ratio of the following two areas

Suppose you have the following triangle $ABC$: with the following properties: $|AB|=4\cdot |AA'|$, $|AC|=4\cdot |CC'|$, $|BC|=4\cdot |BB'|$. I have to find the ratio of the total area of the triangle ...
1
vote
1answer
47 views

Sum of largest two angles

All the inner angles of a 7 sided polygon are obtuse, their sizes in degrees being distinct integers divisible by 9. What is the sum (in degree) of the largest two angles?
8
votes
1answer
891 views

Maximally touching toruses

7 identical cylinders can mutually touch each other, if sufficiently long. For cylinders of different sizes, 8 can touch each other. What is the maximal number of mutually touching toruses? I ...
3
votes
3answers
435 views

number of points on two circles

(sorry I don't know how to add pictures) Two friends argue if larger circles have more points than smaller circles Friend number 1 (a well known argument) Say the circles are concentric. you cannot ...
6
votes
4answers
352 views

Some theorems in euclidean geometry have incomplete proofs

I have seen that, in euclidean geometry, proofs of some theorems use one instance of the 'geometric shape'(on which the theorem is based) to proof the theorem. Like, the proof of 'A straight line ...
5
votes
2answers
1k views

How many triangles in picture

How many triangles in this picture:
2
votes
2answers
576 views

Area puzzle in colored triangle [duplicate]

I have tried to figure out by calculating the area but I got same results for these, so where is gone the hole?
2
votes
1answer
125 views

kaleidoscopic effect on a triangle

Let $\triangle ABC$ and straightlines $r$, $s$, and $t$. Considering the set of all mirror images of that triangle across $r$, $s$, and $t$ and its successive images of images across the same ...
2
votes
4answers
240 views

Higher Dimenional Tic Tac Toe

Here we have a problem that seems very intuitive, but is hard to define mathematically. In Tic Tac Toe, we can find an equivalent of the game in any number of dimensions, it seems. The trick is to ...
3
votes
1answer
721 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
165 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
57 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 ...
86
votes
8answers
3k views

Probability that a stick randomly broken in five places can form a tetrahedron

Edit (March. 2014) This question has been moved to mathoverflow; see here. Randomly break a stick in five places. Question: What is the probability that the resulting six pieces can form a ...
0
votes
1answer
43 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
520 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 ...