# Tagged Questions

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### 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 ...
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 ...
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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 ...
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### 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 ...
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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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) ...
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### 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.
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### 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 $(x^2+y^2)^n$?
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### 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 ...
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?
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### 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 ...
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### 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 ...
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?
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### Volume of remanining part of sphere? [duplicate]

Can some one explain the question? I didn't understand the question clearly.
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 ...
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### 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 ...
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 ...
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### 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.  ...
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### 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 ...
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 ?
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### 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 ...
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### 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 $k$ ...
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 ...
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 ...
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 ...
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### 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 ...
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### 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 ...
184 views

### Question on triangle with heights

Prove that there exists no triangle with heights 4,7, and 10 units. I am completely puzzled.
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 ...
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### 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?
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### 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 ...
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 ...
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 ...
1k views

### How many triangles in picture

How many triangles in this picture:
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?
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 ...
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 ...
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 ...
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### 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 ...
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### 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 ...
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 ...