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.

Pythagoras Hypotenuse Diagram

From Pythagorean Theorem, this length is:

Pythagoras Hypotenuse Expression

Typing the formula is tedious. It’s easier to use the hypotenuse operator.

h  ( shortcut: H )

Enter  3  ⊿ h  4

Pythagoras Hypotenuse Display

Sometimes we know the hypotenuse but we need to find the other side:

Pythagoras Adjacent Diagram

The length of adjacent is:

Pythagoras Adjacent Expression

The adjacent function makes this easy.
It is the secondary function of ⊿ h , accessible via shift (⇧).

=  h  =  ⇧H

Enter  5 3

Pythagoras Adjacent Display

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.

Geometry Distance

The distance d is the hypotenuse. Using Pythagorean theorem:

Geometry Distance Pythorean Theorem

We can use the hypotenuse operator (⊿ ), this simplifies to

Geometry Distance Hypotenuse Expression

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)

For example

Geometry Distance Diagram Numeric

Just enter (3, 2) ⊿  (7, 5)

Geometry Distance Example Numeric

Alternatively you can enter (3; 2) ⊿  (7; 5)

Geometry Distance Example Numeric Alternative

Also known as the dot product. Hence you use the dot ( • ) operator.

Shortcut:  . 

To calculate Geometry Dot Product enter  (1, 2) • (3, 4)

Geometry Dot Product 2d

Here is a 3D example:

Geometry Dot Product 3d

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 Vector (1,2)andVector (3,4)
Enter  (1, 2) (3, 4)

Geometry Vector Angle

* 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:

Geometry Absolute 4D