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◀— math.math

Mathematical Tools

Here's a set of useful mathematical tools which you may find helpful in various situations.
A few comments regarding the tools:

  • If you encounter the expression "NaN", it is the abbreviation for "Not a Number"; in most cases, this means you haven't filled all the necessary boxes. Otherwise, it means your result indeed isn't a number.
  • Sometimes javascript fails to precisely approximate decimal expansions in the results, so it is recommended to trust up to 8-10 digits after the decimal point. If you know a solution to this, please contact me.

Every tool has an explanation below it with more information linked. You can always return to the top by clicking on the small "return to top" button under each tool.


Fraction Simplifier

Karnit mikitiektar:
(koskja iwedeku (enter) NUMERATOR)
———
(koskja iwedeku (enter) DENOMINATOR)

Mikitiani karnit:
NaN
——
NaN
Hy konu burjen THE SAME osmijka, semenek se karnit ha igzek tersoek mikitiani.

Gnamseka:

To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common factor.


Greatest Common Factor

Makor #1:
Makor #2:

VWH:

Gnamseka:

For two numbers A and B, a common factor of A and B is a number C such that both A/C and B/C are natural numbers. The Greatest Common Factor (or Divisor) is the biggest C.


Lowest Common Multiple

Makor #1:
Makor #2:

LWL:

Gnamseka:

For two numbers A and B, a common multiple of A and B is a number C such that both C/A and C/B are natural numbers. The Lowest (or Least, or Smallest) Common Multiple is the smallest C.


Degree to Radian Converter

VALUE DEGREEdak: °

VALUE RADIANdak:

Gnamseka:

Radians are a different way to measure angles based on the circle's perimeter - 360 degrees are equal to 2π radians. To convert degrees to radians, all you have to do is multiply by π and divide by 180°.


Radian to Degree Converter

VALUE RADIANdak: °

VALUE DEGREEdak:

Gnamseka:

Degrees are a unit of measurement in which one full rotation is 360°. To get back from radians to degrees, you just need to do the reverse operation - multiply by 180° and divide by π.


Vector Length (magnitude)

Orynus COORDINATES:
x = y =

Ulur:

Gnamseka:

To find the magnitude of the vector, think of x and y coordinates as the lengths of legs of a right triangle, where the hypotenuse is the vector length itself. Apply the Pythagorean theorem to evaluate the magnitude.


Cartesian to Polar Vector Converter

CARTESIAN opul:
x =
y =

Mekheli opul:
r =
θ =

Gnamseka:

To convert Cartesian coordinates to polar coordinates, we need to separately evaluate the radius r and the angle θ. The radius is the same as the vector's length, so we just apply the vector length formula to get it. To get θ, we look for the angle whose tangent equals y over x.

Side note: You may also use this as a point converter.


Polar to Cartesian Vector Converter

Mekheli opul:
r =
θ = °

CARTESIAN opul:
x =
y =

Gnamseka:

In order to convert polar coordinates to Cartesian coordinates, think of x, y and r as the sides of a right triangle, where r is the hypotenuse. Use two trigonometric functions, cosine and sine, to find the values of x and y respectively.

Side note: You may also use this as a point converter.


Distance Between Points

Hurik 1:
x = y =
Hurik 2:
x = y =

Ulur:

Gnamseka:

To find the distance between two points, we first have to find the distance between the X coordinates (dx) and Y coordinates (dy) of the points. After that, we apply the Pythagorean theorem (dx and dy are the legs of a right triangle, and the distance between A and B is the hypotenuse) and evaluate the square root of the sum of dx squared and dy squared.


Midpoint

Hurik 1:
x = y =
Hurik 2:
x = y =

Elhur hurik: (, )

Gnamseka:

In order to find the coordinates of a point between two points - the midpoint - we take the mean of the X coordinates of both points and Y coordinates of both points separately.


Distance Between (two parallel) Lines

SLOPE-INTERCEPT sikist opulson:
y1 = x +
y2 = x +

Ulur:

Wakji sikist opulson:
Sikist 1: x + y + = 0
Sikist 2: x + y + = 0

Ulur:

Gnamseka:

The shortest segment which is a distance between two parallel lines is part of a line perpendicular to the two. We use this fact to find the general formula for coordinates of two points, where each of the points belongs to one of the parallel lines and the same perpendicular line. After that, we apply the distance between points formula to find and apply the formula for distance between the two lines.


Distance Between a Line and a Point

Wakji sikist opulson:
y1 = x + y +
y2 = (, )

Ulur:

Gnamseka:

To get the formula for the distance between a point and a line, we need to use the properties of a triangle where the height is the distance between the line and the point and the other two vertices are the points of intersections of the line with X and Y axes.


Complex Division (rectangular form)

z1 = + i
z2 = + i

Osmijka:

Gnamseka:

Complex division is more difficult than addition, subtraction or multiplication (hence I made this tool). To divide two complex numbers in rectangular form, you need to multiply the number in the denominator by its complex conjugate. To keep the same value, you also need to multiply the numerator. After a bit of simplyfing, you get the result.


Complex Division (polar form)

z1 = *[cos() + i*sin()]
z2 = *[cos() + i*sin()]

Osmijka:

Gnamseka:

Dividing complex numbers in polar form is a bit easier than in rectangular form. The magnitudes can be divided separately from the rest of the number. The arguments of the cosine and sine functions can be subtracted from one another (click on the link below to see why).


Complex Number Rectangular to Polar Form Converter

z: + i

Osmijka:

Gnamseka:

To convert a complex number from rectangular form to polar form, we need to find the magnitude and angle of the complex number. To find the magnitude, apply the Pythagorean theorem (for complex number z = a + bi and magnitude r, r2 = a2 + b2). To find the angle, apply the tangent function (tan θ = b/a).


Complex Number Polar to Rectangular Form Converter

z: *[cos() + i*sin()]

Osmijka:

Gnamseka:

To convert a complex number from polar to rectangular form, use the properties of a right triangle created from the x & y coordinates and the magnitude. Namely, apply the definition of cosine to find x, and same with sine and y.


Here's a few great math tools made by different people which I highly recommend.


Desmos

Desmos Graphing Calculator

Desmos is a great graphing site which offers graphing functions, equations, inequalities, plotting tables of data, evaluating equations, exploring changes with parameters and more. You can sign up to save and share your graphs. I've been using it for many years and you can see my creations in the Graphs section.


Desmos

WolframAlpha

WolframAlpha is a unique engine for computing answers and providing knowledge, not only about mathematics. Among others, it can solve any equation or plot any function.

If you know any other great math tools, you can tell me about them and I'll consider linking them here.


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