Despite the lack of true vector support, Magic Number’s geometric functions can support multiple arguments which act as multi-dimensional vectors.
You can use comma or semicolon for function arguments. For examples:
|Comma||function (3 , 9)|
|Semicolon||function (3 ; 9)|
This is the longest side of a right-angled triangle.
From Pythagorean Theorem, this length is:
Typing the formula is tedious. It’s easier to use the hypotenuse operator.
( shortcut: H )
Sometimes we know the hypotenuse but we need to find the other side:
The length of adjacent is:
The adjacent function makes this easy.
It is the secondary function of , accessible via shift (⇧).
Enter 5 3
Adjacent is not fussy about the order, you can also enter 3 5.
Before we show you the way, let’s look at the math.
The distance d is the hypotenuse. Using Pythagorean theorem:
We can use the hypotenuse operator (⊿ ), this simplifies to
Of course we still need to calculate a and b where
a = x₂ – x₁ and b = y₂ – y₁
Well not anymore. The hypotenuse operator can accept your coordinates and do the rest. That is (x₁, y₁) ⊿ (x₂, y₂)
Just enter (3, 2) ⊿ (7, 5)
Alternatively you can enter (3; 2) ⊿ (7; 5)
Also known as the dot product. Hence you use the dot ( • ) operator.
Shortcut: ⌥ .
To calculate enter (1, 2) • (3, 4)
Here is a 3D example:
The polar operator is multi-talented.
( shortcut: < )
Generally, it is used to specify complex number in polar format, in the form of
radius ∠ angle.*
If you have multiple arguments on either side, they will be treated as vectors
and Magic Number will calculate the angle between them.
Let’s find the angle between and
Enter (1, 2) ∠ (3, 4)
* When the radius and angle are complex, they will be also treated as vectors.
Also known as the absolute value.
You find it under Menu ▸ Calculation ▸ Extra Functions ▸ Complex Numbers.
Here is a 4D example: