# Tagged Questions

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### How many blocks are required to make the toy?

A pyramid shaped toy is made by tightly placing cubic blocks of $1\times 1\times 1 cm^3$.The base of the toy is a square $4\times 4cm^2$. The width of each step is $0.5cm$.how many blocks are ...
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### How to find the formula of a function from its graph?

I've got some data points (X/Y coordinates) that were apparently created using a certain formula that I want to reconstruct now. I've only got those points, and I can plot them (e.g. like in this). I ...
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### How to solve this problem using spherical coordinates system?

The question is very simple: Volume inside the solid limited by:$(X^2+Y^2+Z^2=16), (X^2+Y^2=4)$ using SPHERICAL coordinates system. The final answer however can be checked making a "cylindrical ...
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### Fitting shapes of know sizes on another larger shape in diagonal fashion

How can I place shapes of known dimensions (with variation) on a larger shape, when intersection of these shapes is permitted and I must make the biggest gap between them? Please note that I wish to ...
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### 3D Shape with only coplanar faces?

I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it. Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape? ...
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### How you could you change the surface area formula for a cylinder to calculate the curved surface area of the half pipe?

Skateboarders use half pipes for doing tricks. A half-pipe is a half cylinder. Explain how you could manipulate the surface area formula for a cylinder to calculate the curved surface area of the ...
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### What shapes fit evenly inside a Hexagon

So I'm designing a board game that uses a number of adjacent hexagonal boards. These boards need to be divided up into spaces (tiles) that players move through. I've been playing with using Hexagons ...
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### Divide a square into different parts

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with geometry, which perhaps yields the shortest, simplest proofs, but other ...
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### How to find the center of a log spiral?

Given just a few points on a log spiral, how to find the center? Considering that the circle is a degenerate case of the log spiral, is there a way to generalize the method for finding circle centers ...
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### Arrange 1-12 around a circle

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with plain old algebra, which yields the shortest, simplest proofs, but other ...
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### How to solve this riddle?

How to solve this riddle? All rooms have the same shape and size. Every room has one entrance, and two exits: one on the left, and one on the right (on opposite directions). Both exits lead to a ...
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### A quadrilateral drawn in the complex plane, Show that ABCD is a square if and only if $i(a-c) = (b-d)$.

A quadrilateral drawn in the complex plane has vertices $A,B,C,D$, labelled anticlockwise. These vertices are represented, respectively, by the complex numbers a, b, c, and d. Show that ABCD is a ...
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### Shape of generalized helix

This is a homework assignment that I fail to understand. The problem is to find the shape of a generalized helix $r=r(s)$ when the fixed vector is $v=(0,0,1)$ and $r(0)=0$. I have found forms that ...
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### What do you call a torus with a center?

This may be a dumb question, but what is a torus with a center called? (Imagine a doughnut, without it's center taken out.)
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### Bisecting line segments in a tetrahedron. [closed]

Suppose that $OABC$ is a regular tetrahedron with base $ABC$. Suppose further that $T$ is the mid-edge of $AC$, $Q$ is the mid-edge of $OB$, $P$ is the mid-edge of $OA$, and $U$ is the mid-edge of ...
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### Relationship between the side lengths of a tetrahedron and an inscribed tetrahedron with vertices at the centroids

Suppose that $OABC$ is a regular tetrahedron with sides having centroids $\lbrace E,F,G,H\rbrace$ also forming a regular tetrahedron. What is the relationship between the side lengths of $OABC$ and ...
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### I call them squares. They called them arrays. What do they mean?

So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that ...
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### whether any shape can be placed on a tiled surface?

After read "Prove that any shape 1 unit area can be placed on a tiled surface",I think on a surface of equal square tiles where each tile side is 1 unit long,the shape ,less than some constant C>1 ...
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### Finding the missing length

How do i find the ST?? What more information do I need? I used Pythagorean theorem, but I still can't find the answer.