Mathematical tables: typical geometry related formulas
Tables show typical formulas related to geometry such as surface area of various geometric plane shapes, disk curcumference, sphere volume etc.

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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$L:=2~\sqrt{\pi\cdot S}$ ? 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$S:=\frac{1}{2}\cdot{ d}^{2}\cdot\sin\left( \alpha\right)$ ? Rhombus area Show source$S:=\frac{1}{2}\cdot e\cdot f$ ? Square area Show source$S:={ a}^{2}$ ? Square area from diagonal Show source$S:=\frac{{ d}^{2}}{2}$ ? Trapezoid area Show source$S:=\frac{\left( a+ b\right)}{2}\cdot h$ ? Triangle area (general) Show source$S:=\frac{1}{2}\cdot a\cdot h$ ? 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$L:=2\cdot\left( a+ b\right)$ ? Rectangle circumference Show source$L:=2\cdot\left( a+ b\right)$ ? Rhombus circumference Show source$L:=4\cdot a$ ? Square circumference Show source$L:=4\cdot a$ ? Triangle circumference (general) Show source$L:= a+ b+ c$ ? Equilateral triangle circumference Show source$L:=3\cdot a$ ? Isosceles triangle circumference Show source$L:= a+2\cdot b$ ?

# Parallelogram

 Name Formula Legend Parallelogram area Show source$S:= a\cdot h$ ? Parallelogram circumference Show source$L:=2\cdot\left( a+ b\right)$ ?

# Renctangle

 Name Formula Legend Rectangle area Show source$S:= a\cdot b$ ? Rectangle circumference Show source$L:=2\cdot\left( a+ b\right)$ ? Rectangle diagonal Show source$d:=\sqrt{{ a}^{2}+{ b}^{2}}$ ? Rectangle area from diagonal Show source$S:=\frac{1}{2}\cdot{ d}^{2}\cdot\sin\left( \alpha\right)$ ?

# Rhombus

 Name Formula Legend Rhombus area Show source$S:=\frac{1}{2}\cdot e\cdot f$ ? Rhombus circumference Show source$L:=4\cdot a$ ?

# Square

 Name Formula Legend Square area Show source$S:={ a}^{2}$ ? Square circumference Show source$L:=4\cdot a$ ? Square diagonal Show source$d:= a~\sqrt{2}$ ? Square area from diagonal Show source$S:=\frac{{ d}^{2}}{2}$ ?

# Trapezoid

 Name Formula Legend Trapezoid area Show source$S:=\frac{\left( a+ b\right)}{2}\cdot h$ ?

# Triangle

 Name Formula Legend Triangle area (general) Show source$S:=\frac{1}{2}\cdot a\cdot h$ ? 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$L:=3\cdot a$ ? Isosceles triangle area Show source$S:=\frac{ b}{4}\cdot\sqrt{4~{ a}^{2}-{ b}^{2}}$ ? Isosceles triangle circumference Show source$L:= a+2\cdot b$ ?

# Equilateral triangle

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

# 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$L:= a+2\cdot b$ ?

# 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. three-dimensional shapes such as cube or cylinder.
• 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 (so-called 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.
• 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 so-called pointless geometry.