diff --git a/README.md b/README.md index f70716b..317a7b2 100644 --- a/README.md +++ b/README.md @@ -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) @@ -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) + + 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) + + 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) + + 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) + + 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) @@ -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) @@ -375,7 +380,7 @@ Other implementations: #### determinant -![pipes3](img/pipes3.png) +![pipes3](img/pipes3.svg) @@ -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) @@ -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) @@ -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) You can also use the "not an element of" symbols `∉` and `∌` like so: -![element3](img/element3.png) +![element3](img/element3.svg) @@ -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) 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) @@ -494,15 +499,15 @@ function square (x) { Sometimes a function is not named, and instead the output is written. - +![function3](img/function3.svg) -![function3](img/function3.png) + 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) @@ -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) Its derivative could be written with a prime `′` symbol: -![prime1](img/prime1.png) +![prime1](img/prime1.svg) diff --git a/img/capital-pi1.svg b/img/capital-pi1.svg new file mode 100644 index 0000000..70a50cb --- /dev/null +++ b/img/capital-pi1.svg @@ -0,0 +1,22 @@ + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/element1.svg b/img/element1.svg new file mode 100644 index 0000000..a35e7a1 --- /dev/null +++ b/img/element1.svg @@ -0,0 +1,34 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/element2.svg b/img/element2.svg new file mode 100644 index 0000000..6906cc5 --- /dev/null +++ b/img/element2.svg @@ -0,0 +1,34 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/element3.svg b/img/element3.svg new file mode 100644 index 0000000..5f6d3da --- /dev/null +++ b/img/element3.svg @@ -0,0 +1,37 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/function1.svg b/img/function1.svg new file mode 100644 index 0000000..2ee547b --- /dev/null +++ b/img/function1.svg @@ -0,0 +1,14 @@ + + + + + + + + + + + + + + diff --git a/img/function2.svg b/img/function2.svg new file mode 100644 index 0000000..7db1098 --- /dev/null +++ b/img/function2.svg @@ -0,0 +1,23 @@ + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/function3.svg b/img/function3.svg new file mode 100644 index 0000000..5539609 --- /dev/null +++ b/img/function3.svg @@ -0,0 +1,18 @@ + + + + + + + + + + + + + + + + + + diff --git a/img/function4.svg b/img/function4.svg new file mode 100644 index 0000000..01953ce --- /dev/null +++ b/img/function4.svg @@ -0,0 +1,34 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/hat.svg b/img/hat.svg new file mode 100644 index 0000000..b9f454b --- /dev/null +++ b/img/hat.svg @@ -0,0 +1,14 @@ + + + + + + + + + + + + + + diff --git a/img/pipes1.svg b/img/pipes1.svg new file mode 100644 index 0000000..4c62bb3 --- /dev/null +++ b/img/pipes1.svg @@ -0,0 +1,15 @@ + + + + + + + + + + + + + + + diff --git a/img/pipes2.svg b/img/pipes2.svg new file mode 100644 index 0000000..04bf5b1 --- /dev/null +++ b/img/pipes2.svg @@ -0,0 +1,15 @@ + + + + + + + + + + + + + + + diff --git a/img/pipes3.svg b/img/pipes3.svg new file mode 100644 index 0000000..38863d8 --- /dev/null +++ b/img/pipes3.svg @@ -0,0 +1,15 @@ + + + + + + + + + + + + + + + diff --git a/img/pipes4.svg b/img/pipes4.svg new file mode 100644 index 0000000..e602c44 --- /dev/null +++ b/img/pipes4.svg @@ -0,0 +1,15 @@ + + + + + + + + + + + + + + + diff --git a/img/prime1.svg b/img/prime1.svg new file mode 100644 index 0000000..8f74414 --- /dev/null +++ b/img/prime1.svg @@ -0,0 +1,25 @@ + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/sigma1.svg b/img/sigma1.svg new file mode 100644 index 0000000..6014feb --- /dev/null +++ b/img/sigma1.svg @@ -0,0 +1,24 @@ + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/sigma2.svg b/img/sigma2.svg new file mode 100644 index 0000000..f95eecc --- /dev/null +++ b/img/sigma2.svg @@ -0,0 +1,34 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/img/sigma3.svg b/img/sigma3.svg new file mode 100644 index 0000000..7d918e7 --- /dev/null +++ b/img/sigma3.svg @@ -0,0 +1,38 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +