# Greatest Hits

715k views

### How many squares actually ARE in this picture? Is this a trick question with no right answer?

This is one of those popular pictures on sites like Facebook. I always see a huge variation of answers such as $8, 9, 16, 17, 24, 28, 30, 40, 41, 52,$ etc., yet I've never seen a definitive answer on ...
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603k views

### Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain but are ...
1 vote
201k views

### Simplification of: AB + A'C + BC in boolean algebra

I am trying to understand the simplification of the boolean expression: AB + A'C + BC I know it simplifies to A'C + BC And I understand why, but I cannot figure out how to perform the ...
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635k views

### What is the difference between independent and mutually exclusive events?

Two events are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't change the probability of the other. Are these ...
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327k views

### Meaning of coprime = (relatively) prime = mutually prime

I've never encountered this question in any of my math classes and it just shows up randomly in my comsci class with no further info about it. I've wiki'ed it, but can't even understand that. Could ...
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370k views

### Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

I need help with this integral: $$I=\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right)\ \mathrm dx.$$ The integrand graph looks like this: $\hspace{1in}$ The ...
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481k views

### Easy way of memorizing values of sine, cosine, and tangent

My math professor recently told us that she wanted us to be able to answer $\sin\left(\frac{\pi }{2}\right)$ in our head on the snap. I know I can simply memorize the table for the test by this Friday,...
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222k views

### A loss and gain problem

This is a very simple but confusing puzzle. A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase. The lady gives him a $1000$ ...
722k views

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118k views

### Piecewise functions: Got an example of a real world piecewise function?

Looking for something beyond a contrived textbook problem concerning jelly beans or equations that do not represent anything concrete. Not just a piecewise function for its own sake. Anyone?
560k views

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186k views

### What is the perimeter of a sector?

I don't understand this. So we have: \begin{align} r &= 12 \color{gray}{\text{ (radius of circle)}} \\ d &= 24 \text{ (r}\times2) \color{gray}{\text{ (diameter of circle)}} \\ c &= 24\pi \...
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515k views

### Difference between "≈", "≃", and "≅"

In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators ...
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375k views

### Probability of getting exactly 2 heads in 3 coins tossed with order not important?

I have been thinking of this problem for the post 3-4 hours, I have come up with this problem it is not a home work exercise Let's say I have 3 coins and I toss them, Here order is not important ...
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542k views

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### What is the importance of eigenvalues/eigenvectors?

What is the importance of eigenvalues/eigenvectors?
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332k views

### Sxx in linear regression

What is the meaning of the symbols $S_{xx}$ and $S_{xy}$ in simple linear regression? I know the formula but what is the meaning of those symbols?
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182k views

### In which order do I graph transformations of functions?

In which order do I graph transformations of functions? The 6 function transformations are: Vertical Shifts Horizontal Shifts Reflection about the x-axis Reflection about the y-axis Vertical ...
307k views

### Proof that $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$

Why is $1+2+3+4+\ldots+n = \dfrac{n\times(n+1)}2$ $\space$ ?
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232k views

### What is the difference between Fourier series and Fourier transformation?

What's the difference between Fourier transformations and Fourier Series? Are they the same, where a transformation is just used when its applied (i.e. not used in pure mathematics)?
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