Beta version#
BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !
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Disk and circle#
Name  Formula  Legend 
Disk area surface  Show source$S=\pi \cdot R^{2}$ 

Disk or circle circumference  Show source$L=2~\pi \cdot R$ 

Disk radius from area surface  Show source$R=\sqrt{\frac{S}{\pi}}$ 

Disk radius from area  Show source$L=2 \cdot \sqrt{\pi \cdot S}$ 

Disk (circle) circumference from circumference  Show source$R=\frac{L}{2~\pi}$ 

Disk (circle) area from circumference  Show source$S=\frac{L^{2}}{4~\pi}$ 

Surface areas of plane shapes#
Name  Formula  Legend 
Disk area surface  Show source$S=\pi \cdot R^{2}$ 

Parallelogram area  Show source$S=a \cdot h$ 

Rectangle area  Show source$S=a \cdot b$ 

Rectangle diagonal  Show source$d=\sqrt{a^{2}+b^{2}}$ 

Rectangle area from diagonal  Show source$S=\frac{1}{2}~d^{2} \cdot sin\left(\alpha\right)$ 

Rhombus area  Show source$S=\frac{1}{2}~e \cdot f$ 

Square area  Show source$S=a^{2}$ 

Square area from diagonal  Show source$S=\frac{d^{2}}{2}$ 

Trapezoid area  Show source$S=\frac{a+b}{2} \cdot h$ 

Triangle area (general)  Show source$S=\frac{1}{2}~a \cdot h$ 

Equilateral triangle area  Show source$S=\frac{a \cdot \sqrt{3}}{2}$ 

Isosceles triangle area  Show source$S=\frac{b}{4} \cdot \sqrt{4~a^{2}b^{2}}$ 

Circumference of shapes#
Name  Formula  Legend 
Disk or circle circumference  Show source$L=2~\pi \cdot R$ 

Parallelogram circumference  Show source$L=2~\left(a+b\right)$ 

Rectangle circumference  Show source$L=2~\left(a+b\right)$ 

Rhombus circumference  Show source$L=4~a$ 

Square circumference  Show source$L=4~a$ 

Triangle circumference (general)  Show source$L=a+b+c$ 

Equilateral triangle circumference  Show source$L=3~a$ 

Isosceles triangle circumference  Show source$L=a+2~b$ 

Parallelogram#
Name  Formula  Legend 
Parallelogram area  Show source$S=a \cdot h$ 

Parallelogram circumference  Show source$L=2~\left(a+b\right)$ 

Renctangle#
Name  Formula  Legend 
Rectangle area  Show source$S=a \cdot b$ 

Rectangle circumference  Show source$L=2~\left(a+b\right)$ 

Rectangle diagonal  Show source$d=\sqrt{a^{2}+b^{2}}$ 

Rectangle area from diagonal  Show source$S=\frac{1}{2}~d^{2} \cdot sin\left(\alpha\right)$ 

Rhombus#
Name  Formula  Legend 
Rhombus area  Show source$S=\frac{1}{2}~e \cdot f$ 

Rhombus circumference  Show source$L=4~a$ 

Square#
Name  Formula  Legend 
Square area  Show source$S=a^{2}$ 

Square circumference  Show source$L=4~a$ 

Square diagonal  Show source$d=a \cdot \sqrt{2}$ 

Square area from diagonal  Show source$S=\frac{d^{2}}{2}$ 

Trapezoid#
Name  Formula  Legend 
Trapezoid area  Show source$S=\frac{a+b}{2} \cdot h$ 

Triangle#
Name  Formula  Legend 
Triangle area (general)  Show source$S=\frac{1}{2}~a \cdot h$ 

Triangle circumference (general)  Show source$L=a+b+c$ 

Equilateral triangle area  Show source$S=\frac{a \cdot \sqrt{3}}{2}$ 

Equilateral triangle circumference  Show source$L=3~a$ 

Isosceles triangle area  Show source$S=\frac{b}{4} \cdot \sqrt{4~a^{2}b^{2}}$ 

Isosceles triangle circumference  Show source$L=a+2~b$ 

Equilateral triangle#
Name  Formula  Legend 
Equilateral triangle area  Show source$S=\frac{a \cdot \sqrt{3}}{2}$ 

Equilateral triangle circumference  Show source$L=3~a$ 

Isosceles triangle#
Name  Formula  Legend 
Isosceles triangle area  Show source$S=\frac{b}{4} \cdot \sqrt{4~a^{2}b^{2}}$ 

Isosceles triangle circumference  Show source$L=a+2~b$ 

Some facts#
 Geometry is one of two oldest fields of mathematics (next to arithmetic).
 Geometry examines geometric shapes and their relationships.
 Due to the kind of shapes we deal with, we divide the geometry into two parts:
 planimetry  the part dealing with flat shapes, i.e. those that can be drawn in a 2D plane like square, circle, etc.,
 stereometry  the part dealing with spatial solids, i.e. threedimensional shapes such as cube or cylinder.
 planimetry  the part dealing with flat shapes, i.e. those that can be drawn in a 2D plane like square, circle, etc.,
 The origins of geometry go back to ancient times. The father of geometry in the form we know today is Greek philosopher Euclid. About 300 BC he prioritized knowledge about geometry, which resulted in a dissertation "Elements".
 Euclid's "Elements" are considered one of the first theoretical works in mathematics. Euclid, ordering the previous knowledge, indicated a few the most basic laws (socalled axioms), and then he used them to derive all existing geometry as today's mathematicians do. This is why his work is considered a breakthrough not only for the development of geometry, but mathematics in general.
 The axioms adopted by Euclid were as follows:
 1. To draw a straight line from any point to any point.
 2. To produce a finite straight line continuously in a straight line.
 3. To describe a circle with any centre and distance.
 4. That all right angles are equal to one another.
 5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
 1. To draw a straight line from any point to any point.
 Nowadays, geometry based on the above postulates is called Euclidean geometry. However, over time, mathematicians began to study geometries based on other axioms, removing or modifying selected points from the original list used by Euclid. Such geometries are, for example, Riemann's geometry (removing the Euclidian postulate 5.), used to formulate General relativity of Einstein or socalled pointless geometry.
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