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mattdesl
2015-06-30 19:34:01 -04:00
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README.md
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@@ -100,8 +100,6 @@ var j = x / (2 * k)
The `≅` symbol is for [*congruence*](https://en.wikipedia.org/wiki/Congruence_%28geometry%29). For example, here the line segment AB is congruent with the segment CD.
![equals2](img/equals2.png)
\bar{AB} \cong \bar{CD} -->
## dot & cross
@@ -242,7 +240,7 @@ For other implementations of vector multiplication, cross product, and dot produ
The big Greek "E" (Sigma) is for [Summation](https://en.wikipedia.org/wiki/Summation). In other words: summing up some numbers.
![sigma](img/sigma1.png)
![sigma](img/sigma1.svg)
<!-- \sum_{i=1}^{100}i -->
@@ -266,7 +264,9 @@ var sum = (n * (n + 1)) / 2
Here is another example where the *i*, or the "what to sum," is different:
![sum2](img/sigma2.png)
![sum2](img/sigma2.svg)
<!-- \sum_{i=1}^{100}(2i+1) -->
In code:
@@ -281,7 +281,9 @@ The result of `sum` is `10200`.
The notation can be nested, which is much like nesting a `for` loop. You should evaluate the right-most sigma first, unless the author has enclosed them in parentheses to alter the order.
![sigma3](img/sigma3.png)
![sigma3](img/sigma3.svg)
<!-- \sum_{i=1}^{2}\sum_{j=4}^{6}(3ij) -->
In code:
@@ -302,14 +304,15 @@ The capital Pi or "Big Pi" is very similar to [Sigma](#sigma), except we are usi
Take the following:
![capitalPi](img/capital-pi1.png)
![capitalPi](img/capital-pi1.svg)
<!-- \prod_{i=1}^{6}i -->
In code, it might look like this:
```js
var n = 6
var value = 1
for (var i = 1; i <= n; i++) {
for (var i = 1; i <= 6; i++) {
value *= i
}
```
@@ -324,7 +327,9 @@ These three features all describe the *length* of an object.
#### absolute
![pipes1](img/pipes1.png)
![pipes1](img/pipes1.svg)
<!-- \left | x \right | -->
For a number *x*, `|x|` means the absolute of *x*. In code:
@@ -336,7 +341,7 @@ var result = Math.abs(x)
#### Euclidean norm
![pipes4](img/pipes4.png)
![pipes4](img/pipes4.svg)
<!-- \left \| \mathbf{v} \right \| -->
@@ -344,7 +349,7 @@ For a vector **v**, `‖v‖` is the [Euclidean norm](https://en.wikipedia.org/w
Often this is represented by double-bars to avoid ambiguity with the *absolute* notation, but sometimes you may see it with single bars:
![pipes2](img/pipes2.png)
![pipes2](img/pipes2.svg)
<!-- \left | \mathbf{v} \right | -->
@@ -375,7 +380,7 @@ Other implementations:
#### determinant
![pipes3](img/pipes3.png)
![pipes3](img/pipes3.svg)
<!-- \left |\mathbf{A} \right | -->
@@ -403,7 +408,7 @@ Implementations:
In geometry, the "hat" symbol above a character is used to represent a [unit vector](https://en.wikipedia.org/wiki/Unit_vector). For example, here is the unit vector of **a**:
![hat](img/hat.png)
![hat](img/hat.svg)
<!-- \hat{\mathbf{a}} -->
@@ -443,7 +448,7 @@ Other implementations:
In set theory, the "element of" symbol `∈` and `∋` can be used to describe whether something is an element of a set. For example:
![element1](img/element1.png)
![element1](img/element1.svg)
<!-- A=\left \{3,9,14}{ \right \}, 3 \in A -->
@@ -458,13 +463,13 @@ A.indexOf(3) >= 0
The backwards `∋` is the same, but the order changes:
![element2](img/element2.png)
![element2](img/element2.svg)
<!-- A=\left \{3,9,14}{ \right \}, A \ni 3 -->
You can also use the "not an element of" symbols `∉` and `∌` like so:
![element3](img/element3.png)
![element3](img/element3.svg)
<!-- A=\left \{3,9,14}{ \right \}, 6 \notin A -->
@@ -474,13 +479,13 @@ You can also use the "not an element of" symbols `∉` and `∌` like so:
A function relates an input to an output value. For example, the following is a function:
![function1](img/function1.png)
![function1](img/function1.svg)
<!-- x^{2} -->
We can give this function a *name*. Commonly, we use `ƒ` to describe a function, but it could be named `A(x)` or anything else.
![function2](img/function2.png)
![function2](img/function2.svg)
<!-- f\left (x \right ) = x^{2} -->
@@ -494,15 +499,15 @@ function square (x) {
Sometimes a function is not named, and instead the output is written.
<!-- y = x^{2} -->
![function3](img/function3.svg)
![function3](img/function3.png)
<!-- y = x^{2} -->
In the above example, *x* is the input, the relationship is *squaring*, and *y* is the output.
Functions can also have multiple parameters, like in a programming language. These are known as *arguments* in mathematics, and the number of arguments a function takes is known as the *arity* of the function.
![function4](img/function4.png)
![function4](img/function4.svg)
<!-- f(x,y) = \sqrt{x^2 + y^2} -->
@@ -524,13 +529,13 @@ In code, we typically just assign the variable a more descriptive name, like `tr
For a mathematical [function](#function), the prime symbol often describes the *derivative* of that function. Derivatives will be explained in a future section. Let's take our earlier function:
![function2](img/function2.png)
![function2](img/function2.svg)
<!-- f\left (x \right ) = x^{2} -->
Its derivative could be written with a prime `′` symbol:
![prime1](img/prime1.png)
![prime1](img/prime1.svg)
<!-- f'(x) = 2x -->

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