Geometry

Constant representing the value of π (pi).

Example

julia> PI
3.141592653589793

Point(x, y)
Point(x, y, z)

Structure containing 2D or 3D coordinates.

Examples

julia> p1 = Point(1, 2, 3)
Point(1, 2, 3)

julia> p2 = Point(4, 5)
Point(4, 5, nothing)

circumference(radius)

Calculate circumference given the radius.

Example

julia> circumference(32.50)
204.20352248333654

diameter(radius)

Calculate diameter given the radius.

Example

julia> diameter(17.75)
35.5

radius(diameter)

Calculate radius given the diameter.

Example

julia> radius(54.25)
27.125

area_circle(radius)

Calculate area of a circle given the radius.

Example

julia> area_circle(157)
77437.11731833481

area_cube(side_length)

Calculate area of a cube given the length of a side.

Example

julia> area_cube(42)
10584

area_ellipse(major_semiaxis, minor_semiaxis)

Calculate area of an ellipse given the major and minor semiaxes.

Example

julia> area_ellipse(50.575, 50.419)
8010.875677067962

area_rectangle(height, width)

Calculate area of a rectangle given the height and width.

Example

julia> area_rectangle(15.75, 20)
315.0

area_square(side_length)

Calculate area of a square given the length of a side.

Example

julia> area_square(25.50)
650.25

area_trapezoid(base_length, top_length, height)

Calculate area of a trapezoid given the base length, top length, and height.

Example

julia> area_trapezoid(30.5, 10.5, 20.75)
425.375

area_triangle(base_length, height)

Calculate area of a triangle given the base length and height.

Example

julia> area_triangle(42.5, 32.50)
690.625

perimeter_rectangle(height, width)

Calculate perimeter of a rectangle given the height and width.

Example

julia> perimeter_rectangle(25, 50)
150

perimeter_square(side_length)

Calculate perimeter of a square given the length of a side.

Example

julia> perimeter_square(25)
100

perimeter_triangle(side_a, side_b, side_c)

Calculate perimeter of a triangle given the length of the sides.

Example

julia> perimeter_triangle(10, 20, 30)
60

edges(faces, vertices)

Calculate edges of a convex polyhedron given the faces and vertices.

Example

julia> edges(6, 8)
12

faces(edges, vertices)

Calculate faces of convex polyhedron given the edges and vertices.

Example

julia> faces(12, 8)
6

vertices(edges, faces)

Calculate vertices of a convex polyhedron given the edges and faces.

Example

julia> vertices(12, 6)
8

has_euler_characteristic(edges, faces, vertices)

Determine whether or not a polyhedron has the Euler characteristic given the edges, faces, and vertices.

Examples

julia> has_euler_characteristic(6, 4, 4) # tetrahedron
true

julia> has_euler_characteristic(12, 7, 6) # tetrahemihexahedron
false

pytheorem(leg_a, leg_b)

Calculate (using the Pythagorean theorem) area of the square formed along the hypotenuse of a right triangle given the length of the legs.

Examples

julia> pytheorem(3, 7)
58

julia> hypotenuse_length(3, 7) ^ 2
58

hypotenuse_length(leg_a, leg_b)

Calculate length of a hypotenuse given the length of the legs. The hypotenuse is the longest side of a right triangle and is opposite of the 90° angle.

Examples

julia> hypotenuse_length(4, 7)
8.06225774829855

julia> sqrt(pytheorem(4, 7))
8.06225774829855

leg_length(leg, hypotenuse)

Calculate length of a missing right triangle leg given the lengths of an existing leg and the hypotenuse.

Example

julia> leg_length(4, 8.0623)
7.000048663402277

distance_2d(x1, y1, x2, y2)
distance_2d(p1, p2)

Calculate distance between a pair of 2D points given the coordinates.

Examples

julia> distance_2d(25, 42, 35, 80)
39.293765408777

julia> p1 = Point(25, 42)
Point(25, 42, nothing)

julia> p2 = Point(35, 80)
Point(35, 80, nothing)

julia> distance_2d(p1, p2)
39.293765408777

distance_3d(x1, y1, z1, x2, y2, z2)
distance_3d(p1, p2)

Calculate distance between a pair of 3D points given the coordinates.

Examples

julia> distance_3d(14, 8, 5, 17, 38, 23)
35.11409973215888

julia> p1 = Point(14, 8, 5)
Point(14, 8, 5)

julia> p2 = Point(17, 38, 23)
Point(17, 38, 23)

julia> distance_3d(p1, p2)
35.11409973215888