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math1.lua
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math1.lua
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-- math1.lua, an extension of the math library
-- degrees to radians
function degree_to_radian(deg)
local RADIAN = (math.pi/180)
radian = (deg * RADIAN);
return radian;
end
----------------
-- chance by percentage
-- ?% chance to be true
function chance1(percent)
if percent >= math.random(1, 100) then
return true
end
return false
end
----------------
-- 50% chance to be true
function chance50()
local percent = math.random(0, 1)
if percent == 1 then
return true
end
return false
end
----------------
-- returns your current exp in percentage
function get_exp_percentage(current_exp, exp_to_next_level)
local n = current_exp * 100
local d = exp_to_next_level
local percent = n/d
return tonumber(string.format("%.2f", percent))
end -- print(get_exp_percentage(6, 14).."%") -- 6 out of 14 EXP. You need 14 EXP to reach level 2
----------------
function percent_of(percent, number) -- not quite right
return tonumber("0."..percent) * number
end -- ten_percent_of_100 = percent_of(10, 100) print(ten_percent_of_100)
----------------
-- 2 rows, 3 columns
matrix_1 = {
{1, 2, 3}, -- matrix_1[1]
{4, 5, 6}, -- matrix_2[2]
}
----------------
-- verified!
function makematrix(row, column)
local mt = {}
for i=1, row do
mt[i] = {} -- each row is a table; column is number per table
for n=1, column do
mt[i][n] = 0 -- fill each row with 0's(to set the size of each row)
end
end
mt.row = #mt
mt.column = #mt[1] -- column = size of one row
return mt
end
----------------
function drawmatrix(mt)
for i= 1, #mt do
io.write("row"..i..": ") -- row index(which row?)
for n=1, #mt[1] do
io.write(mt[i][n].." ") -- get the numbers in each row
if n==#mt[1] then -- separate the rows
print("\n") end
end
end
end
----------------
function insertmatrix(num, row, column, mt)
mt[row][column] = num
end
----------------
-- good!
function getrows(mt) -- get number of rows in a matrix
return #mt
end
----------------
-- good!
function getcolumns(mt, row_num)
if not row_num then
row_num = 1
end
return #mt[row_num] -- size of one row
end
----------------
function add(a, b) return a + b end
function subtract(a, b) return a - b end
function multiple(a, b)return a * b end
function divide(a, b) return a / b end
----------------
function actual_mat_add(mt1, mt2)
for r = 1, #mt1 do
for c = 1, mt1.column do
local matrix = m1[r][c] + m2[r][c]
print(matrix)
end
end
end
----------------
-------------- transformations
function translate(tx, ty, tz) -- or move
if not tz then tz=0 end
x = x + tx
y = y + ty
z = z + tz
end
----------------
function rotate(angle, rx, ry, rz)
angle = angle*(math.pi/180) -- angles are measured in radians
if _2d then
x = x*(math.cos(angle)) - y*(math.sin(angle))
y = x*(math.sin(angle)) + y*(math.cos(angle))
end
if _3d then
if rx == 1 then
x=x
y = y*(math.cos(angle)) - z*(math.sin(angle))
z = y*(math.sin(angle)) + z*(math.cos(angle))
end
if ry == 1 then
x=x*(math.cos(angle)) + z*(math.sin(angle))
y =y
z= x*(math.sin(angle)) - z*(math.cos(angle))
end
if rz == 1 then
x=x*(math.cos(angle)) - y*(math.sin(angle))
y= x*(math.sin(angle)) + y*(math.cos(angle))
z=z
end
end
end -- eof
----------------
function scale(sf, sx, sy, sz)
if _2d then
sx = sf
sy = sx
x = x*sx
y = x*sy
end
if _3d then
if sx == 1 then
x=x*sf
end
if sy == 1 then
y=y*sf
end
if sz == 1 then
z=z*sf
end
end
end
----------------
function reflect(o) -- or flip
if _2d then
if o == "h" then-- horizontal flip requested
if x == x then -- x is a positive
x=-x -- change x to a negative
end
if x == -x then -- x is a negative
x=math.abs(x) -- change x to a positive
end
end
if o == "v" then -- vertical flip requested
if y==y then -- y is a positive
y=-y -- change y to a negative
end
if y==-y then -- y is a negative
y=math.abs(y) -- change y to a positive
end
end
end
if _3d then -- ??
if o == "h" then
end
if o == "v" then
end
end
end
----------------
function shear(shx, shy, shz)
if _2d then
x = x + (shx*y) -- if shx is 0, no shear on x axis
y = y + (shy*x) -- if shy is 0, no shear on y axis
end
if _3d then
-- xz direction
x = x + (shx*y)
y = y
z = z + (shz*y)
-- yz direction
x = x
y = y + (shy*x)
z = z + (shz*x)
end
end
----------------
-- fractions
function fraction_add(a, b, c, d) -- n is numerator, d is denomenator
local n = (a*d) + (b*c) -- numerator
local d = (b*d)
print(tostring(n.."/"..d))
end
----------------
function fraction_sub(a, b, c, d)
local n = (a*d) - (b*c)
local d = (b*d)
print(tostring(n.."/"..d))
end
----------------
fraction_mul = function(a, b, c, d)
local n = (a*c) -- multiply directly - numerator with numerator and denomenator with denominator
local d = (b*d)
print(tostring(n.."/"..d))
end
----------------
fraction_div = function(a, b, c, d)
local n = (a*d) -- flip the right-sided fraction then multiply
local d = (b*c)
print(tostring(n.."/"..d))
end
----------------
--- inequalities
function is_equal(a, b)
if a == b then
return true
end
return false
end
----------------
function is_less_than(a, b) end
----------------
function is_greater_than(a, b)
if a > b then
return true
end
return false
end
----------------
function is_less_than_or_equal(a, b)
if a >= b then
return true
end
return false
end
----------------
function is_greater_than_or_equal(a, b)
if a <= b then
return true
end
return false
end
----------------
-- factors
function get_factors(n) -- 4 = 1 x 4 and 2 x 2
for i = 0, 100 do
for f = 0, 100 do
if n == i*f then
print(i..", "..f)
end
end
end
end
----------------
function get_prime_factorization(n) -- 12 = 2 x 2 x 3
for i = 0, 100 do
for f = 0, 100 do
for p = 0, 100 do
if i ~= 1 and p ~= 1 and f ~= 1 then
if n == i*f*p then
print(i..", "..f..", "..p)
break
end
end
end
end
end
end
----------------
-- prime numbers - only factors are 1 and itself
function is_prime_number(n)
for i = 0, 1000 do
for p = 0, 1000 do
--if i == n and p == 1 or
if i == 1 and p == i then
return true
end
end
end
return false
end
----------------
-- Mixed number to improper fraction
function mixed_number_to_improper_fraction(x, a, b)
answer = ((b)*(x)) + a
--answer = answer / b
return answer.."/"..b
end
----------------
to_improper = mixed_number_to_improper_fraction
----------------
function is_pythagorean_triple(a, b, c) -- 3, 4, 5
if (math.pow(a, 2) + math.pow(b, 2)) == math.pow(c, 2) then
return true
end
return false
end
----------------
-- distance formula
function calculate_distance(x1, y1, x2, y2)
return math.sqrt((x2 - x1)*(2) + (y2 - y1)*(2))
end
----------------
function sides_to_name(side)
if side == 3 then
side = "Triangle"
end
if side == 4 then side = "Quad" end
if side == 5 then side = "Pentagon" end
if side == 6 then side = "Hexagon" end
if side == 7 then side = "Heptagon" end
if side == 8 then side = "Octagon" end
if side == 10 then side = "Decagon" end
if side == 12 then side = "Dodecagon" end
----
if side == 9 then side = "Nonagon, Enneagon" end
if side == 11 then side = "Undecagon, Hendecagon" end
if side == 13 then side = "Tridecagon, Triskaidecagon" end
if side == 14 then side = Tetradecagon, Tetrakaidecagon end
if side == 15 then side = "Pentadecagon, Pentakaidecagon" end
if side == 16 then side = Hexadecagon, Hexakaidecagonend end
if side == 17 then side = "Heptadecagon, Heptakaidecagon" end
if side == 18 then side = Octadecagon, Octakaidecagon end
if side == 19 then side = "Enneadecagon, Enneakaidecagon" end
if side == 20 then side = Icosagon end
if side == 30 then side = "Triacontagon" end
if side == 40 then side = Tetracontagon end
if side == 50 then side = Pentacontagon end
if side == 60 then side = "Hexacontagon" end
if side == 70 then side = Heptacontagon end
if side == 80 then side = Octacontagon end
if side == 90 then side = "Enneacontagon" end
if side == 100 then side = Hectogon, Hecatontagon end
if side == 1000 then side = "Chiliagon" end
if side == 10000 then side = Myriagon end
end
function get_area(shape)
if shape.type == "SQUARE" then
square.area = math.pow(6,6)
end
end
function power(n, power_)
math.pow(n, power_)
end
function polygon_type(polygon)
if equal_sides_and_same_lenght then
return "Regular"
end
if equal_angles then
return "Equiangular"
end
if equal_side_lengths then
return "Equilateral"
end
end
function decimal_place(n)
if string.len(n) == 1 then
return "Ones"
end
--[[
1 - ones
2 - tens
3 - hundreds
4 - thousands
5 - ten thousands
6 - hundred thousands
7 - millions
8 - ten millions
9 - hundred millions
10 - billion
11 - ten billion
12 - hundren billion
13 - trillion(1 with 12 zeros)
16 - quadrillion(1 with 15 zeros)
sextillion 1 with 21 zeros
septillion 1 with 24 zeros
octillion 1 with 27 zeros
googol 1 with 100 zeros
googolplex 1 with a googol of zeros
1, 000, 000, 000, 000(one trillion)
]]--
end
-- CONVERSIONS
function percent_to_decimal(number, percent)
-- convert the percentage to decimals
decimal = tonumber("0."..percent)
result = (decimal*number)
return result
end
function number_to_roman_numerals() end
--------------------------------
function squared(a)
return a*a
end
function cubed(a)
return a*a*a
end
--VALID! BUT NEEDS IMPROVEMENTS
function squareroot(a) -- 9
-- ?? x ?? = a
-- math.sqrt(a) -- THIS COULD HAVE BEEN EASIER
for n = 0, 99999 do
if squared(n) == a then
sq_root = n
else
print(a.." is a surd.") -- meaning it cannot be simplified any further
end
end
return sq_root
end
function pythag(a, b, c)
a = squared(a)
b = squared(b)
result = a + b
if result == squared(c) then
print("You are right")
print(a.." + "..b.." = "..result)
else
print(a.." + ".. b.." is not equal to "..squared(c))
print(a.." + "..b.." = "..result)
end
if c == nil then
c = squared(c)
print(a.."^2 + "..b.."^2 is "..squared(c))
--return result
end
end
--[[
3 dimension
0 point(0d) - also called a vertex, vector
1 line(1d) - between 2 points
2 square(2d) -- plane
3 cube(3d) --solid
planes are flat 2d surfaces like a square circle triangle, etc
triangle = 3 dots
x-axis = left(-), right(+)=(horizontal)
y-axis = up(+), down(-)=(vertical)
z-axis = foward(-), backwards(+), length(diagonal)
origin = 0, 0, 0
coordinates = {
x = 0
y = 0
z = 0
}
z-axis can push foward or backwards! DEPTH
]]--
-- NO EQUAL SIDES
function scalene(triangle)
angle_a = triangle.angle_a
angle_b = triangle.angle_b
angle_c = triangle.angle_c
if triangle.angle_a ~= angle_b or
triangle.angle_a ~= angle_c or
triangle.angle_b ~= angle_a or
triangle.angle_b ~= angle_c or
triangle.angle_c ~= angle_a or
triangle.angle_c ~= angle_b then
print("The triangle is scalene.")
return true
end
end
-- ONLY TWO EQUAL SIDES
function isosceles(triangle)
-- ANGLE A AND B ARE EQUAL, BUT NOT C
if triangle.angle_a == triangle.angle_b and triangle.angle_a ~= triangle.angle_c or
-- ANGLE B AND C ARE EQUAL, BUT NOT A
triangle.angle_b == triangle.angle_c and triangle.angle_b ~= triangle.angle_a or
-- ANGLE C AND A ARE EQUAL, BUT NOT B
triangle.angle_c == triangle.angle_a and triangle.angle_c ~= triangle.angle_b then
print("The triangle is an isoceles.")
return true
end
end
-- MUST HAVE THREE EQUAL SIDES
function equailateral(triangle)
-- A IS B AND B IS C
if triangle.angle_a == triangle.angle_b and triangle.angle_b == triangle.angle_c then
print("The triangle is equilateral.")
return true
end
end
----------------------------------------
--AT LEAST ONE ANGLE MUST BE NINETY DEGREES
function right(triangle)
ninety_deg = 90
if triangle.angle_a == ninety_deg or triangle.angle_b == ninety_deg or triangle.angle_c == ninety_deg then
print("The triangle has a right angle.")
return true
end
end
-- ALL ANGLES MUST BE LESS THAN NINETY DEGREES
function acute(triangle)
ninety_deg = 90
if triangle.angle_a < ninety_deg and triangle.angle_b < ninety_deg and triangle.angle_c < ninety_deg then
print("The triangle has acute angles.")
return true
end
end
--AT LEAST ONE ANGLE MUST BE ABOVE NINETY DEGREES
function obtuse(triangle)
if triangle.angle_a > ninety_deg or triangle.angle_b > ninety_deg or triangle.angle_c > ninety_deg then
print("The triangle has an obtuse angle.")
return true
end
end
--[[
polygons = 2d shapes.
meshs(model) = 3d shapes.
]]--
INFINITY = math.pi
Polygon = {}
function Polygon.new(type_, sides, points, faces, edges)
local polygon = {}
polygon.type = type_
if polygon.type == CIRCLE then
polygon.side = INFINITY
end
if polygon.type == TRIANGLE then
polygon.side = 3
end
if polygon.type == SQUARE then
polygon.side = 4
end
if polygon.type == PENTAGON then
polygon.side = 5
end
if polygon.type == HEXAGON then
polygon.side = 6
end
if polygon.type == HEPTAGON then
polygon.side = 7
end
if polygon.type == OCTAGON then
polygon.side = 8
end
if polygon.type == NONAGON then
polygon.side = 9
end
if polygon.type == DECAGON then
polygon.side = 10
end
if polygon.type == RECTANGLE then
polygon.side = 4
end
if polygon.type == OVAL then
polygon.side = INFINITY
end
if polygon.type == RHOMBUS then
polygon.side = 4
end
if polygon.type == HEART then
polygon.side = "??"
end
if polygon.type == STAR then
polygon.side = "??"
end
if polygon.type == DIAMOND then
polygon.side = "??"
end
if polygon.type == CRESCENT then
polygon.side = "?"
end
setmetatable(polygon, {__index = Polygon})
return polygon
end
function rotate(object, x, y, z)
end
function rotate2d(degree)
end
function translate(object, x, y, z)
object.x = object.x + x
object.y = object.y + y
object.z = object.z + z
end
function reflect(object, x, y, z) -- flip
end
function scale(degree)
end
-- move 10 units right, 30 units up
--translate(polygon, 10, 30)
function reshapeToSphere(object)
end
function addTexture(object, texture)
end
function trangulate(object)
end
function wireframe(object)
end
function EclipseArea(a, b)
local area = math.pi *a *b
end
-- ALWAYS EQUAL TO TWO
function eulerFormula(object)
e = object.face + objet.vertex - object.edge
return e
end
--[[
CUBE 6F 12E 8V
CYINDER 3F 2E 0V
CONE 2F 1E 1V
SPHERE 1F 0E 0V
PYRAMID
TORUS -- RING
convergent
]]--
-- math.modf(10.4) removes the fraction 0.4 from the 10 and returns the 10
--[[
VELOCITY = SPEED OF SOMETHING IN A GIVEN DIRECTION
RATE IN WHICH AN OBJECT CHANGES ITS POSITION, VECTOR QUUANTITY
SPEED = SCALAR QUANTITY, HOW FAST AN OBJECT MOVES
]]--
--[[
object = {}
-- VELOCITY ALWAYS REQUIRE A DIRECTION
function velocity(object, rate, direction)
v = distance(how much ground has been covered) + direction / rate
end
velocity(object, 50miles, "north"); -- if 0, you are not changing your position, but can still be moving.
function speed(rate)
end
speed(object, 10.0)
-- speed = distance / time -- (HOW LONG IT TAKES YOU TO GET THERE)HOW FAR YOU GO, LOSING(DIVIDED BY) SOME TIME IT TAKES TO GET THERE
-- velocity = displacement / time(HOW FAR YOU MOVE BETWEEN TIMES)
-- OR velocity = displacement + direction / time
-- object that returns to its original location has no velocity
-- velocity = distance(50 miles) and direction(west) / change in time(use up 4 hours) ex. it takes 4 hours to go 50 miles to the west
-- velocity = 50 miles / 4 hours = 12.5 miles per every he went(move 12.5 miles each hour)
-- final_velocity = inital_velocity + (acceleration * time)
--5km to get to the north in 1 hour
seconds = 1.0
distance_to_school = 2 miles
velocity = distance_to_school / 30 minutes -- how long took it took to get to school
-- it takes me 30 minutes to get to school, and I walked two miles to get
--there, so that is 0.0666666666666667 miles every minute I walked
]]--
----------------- FORMULAS ---------------------
-- AREA
function get_area(shape)
if shape.type == "SQUARE" then
area = (side_len*side_len)
end
-- rectangle = ab
--[[
parallelogram = bh
square = a 2
rectangle = ab
parallelogram = bh
trapezoid = h/2 (b1 + b2)
circle = pi r 2
ellipse = pi r1 r2
triangle = 1/2(b*h)
equilateral triangle = sqrt(3) / 4(a*a)
]]--
end
-- VOLUME
function get_volume(shape)
--[[
cube = a 3
rectangular prism = a b c
irregular prism = b h
cylinder = b h = pi r 2 h
pyramid = (1/3) b h
cone = (1/3) b h = 1/3 pi r 2 h
sphere = (4/3) pi r 3
ellipsoid = (4/3) pi r1 r2 r3
]]--
end
function get_surface_area(shape)
--[[
Surface Area of a Cube = 6 a 2
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
]]--
end
if not dokun then
function Vector1(x) return x end
function Vector2(x, y) return x, y end
function Vector3(x, y, z) return x, y, z end
function Vector4(x, y, z, a) return x, y, z, a end
end