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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

NameFormulaLegend
Disk area surfaceShow sourceS:=πR2 S:=\pi\cdot{ R}^{2}?
Disk or circle circumferenceShow sourceL:=2 πR L:=2~\pi\cdot R?
Disk radius from area surfaceShow sourceR:=Sπ R:=\sqrt{\frac{ S}{\pi}}?
Disk radius from areaShow sourceL:=2 πS L:=2~\sqrt{\pi\cdot S}?
Disk (circle) circumference from circumferenceShow sourceR:=L2 π R:=\frac{ L}{2~\pi}?
Disk (circle) area from circumferenceShow sourceS:=L24 π S:=\frac{{ L}^{2}}{4~\pi}?

Surface areas of plane shapes

NameFormulaLegend
Disk area surfaceShow sourceS:=πR2 S:=\pi\cdot{ R}^{2}?
Parallelogram areaShow sourceS:=ah S:= a\cdot h?
Rectangle areaShow sourceS:=ab S:= a\cdot b?
Rectangle diagonalShow sourced:=a2+b2 d:=\sqrt{{ a}^{2}+{ b}^{2}}?
Rectangle area from diagonalShow sourceS:=12d2sin(α) S:=\frac{1}{2}\cdot{ d}^{2}\cdot\sin\left( \alpha\right)?
Rhombus areaShow sourceS:=12ef S:=\frac{1}{2}\cdot e\cdot f?
Square areaShow sourceS:=a2 S:={ a}^{2}?
Square area from diagonalShow sourceS:=d22 S:=\frac{{ d}^{2}}{2}?
Trapezoid areaShow sourceS:=(a+b)2h S:=\frac{\left( a+ b\right)}{2}\cdot h?
Triangle area (general)Show sourceS:=12ah S:=\frac{1}{2}\cdot a\cdot h?
Equilateral triangle areaShow sourceS:=a32 S:=\frac{ a\cdot\sqrt{3}}{2}?
Isosceles triangle areaShow sourceS:=b44 a2b2 S:=\frac{ b}{4}\cdot\sqrt{4~{ a}^{2}-{ b}^{2}}?

Circumference of shapes

NameFormulaLegend
Disk or circle circumferenceShow sourceL:=2 πR L:=2~\pi\cdot R?
Parallelogram circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)?
Rectangle circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)?
Rhombus circumferenceShow sourceL:=4a L:=4\cdot a?
Square circumferenceShow sourceL:=4a L:=4\cdot a?
Triangle circumference (general)Show sourceL:=a+b+c L:= a+ b+ c?
Equilateral triangle circumferenceShow sourceL:=3a L:=3\cdot a?
Isosceles triangle circumferenceShow sourceL:=a+2b L:= a+2\cdot b?

Parallelogram

NameFormulaLegend
Parallelogram areaShow sourceS:=ah S:= a\cdot h?
Parallelogram circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)?

Renctangle

NameFormulaLegend
Rectangle areaShow sourceS:=ab S:= a\cdot b?
Rectangle circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)?
Rectangle diagonalShow sourced:=a2+b2 d:=\sqrt{{ a}^{2}+{ b}^{2}}?
Rectangle area from diagonalShow sourceS:=12d2sin(α) S:=\frac{1}{2}\cdot{ d}^{2}\cdot\sin\left( \alpha\right)?

Rhombus

NameFormulaLegend
Rhombus areaShow sourceS:=12ef S:=\frac{1}{2}\cdot e\cdot f?
Rhombus circumferenceShow sourceL:=4a L:=4\cdot a?

Square

NameFormulaLegend
Square areaShow sourceS:=a2 S:={ a}^{2}?
Square circumferenceShow sourceL:=4a L:=4\cdot a?
Square diagonalShow sourced:=a 2 d:= a~\sqrt{2}?
Square area from diagonalShow sourceS:=d22 S:=\frac{{ d}^{2}}{2}?

Trapezoid

NameFormulaLegend
Trapezoid areaShow sourceS:=(a+b)2h S:=\frac{\left( a+ b\right)}{2}\cdot h?

Triangle

NameFormulaLegend
Triangle area (general)Show sourceS:=12ah S:=\frac{1}{2}\cdot a\cdot h?
Triangle circumference (general)Show sourceL:=a+b+c L:= a+ b+ c?
Equilateral triangle areaShow sourceS:=a32 S:=\frac{ a\cdot\sqrt{3}}{2}?
Equilateral triangle circumferenceShow sourceL:=3a L:=3\cdot a?
Isosceles triangle areaShow sourceS:=b44 a2b2 S:=\frac{ b}{4}\cdot\sqrt{4~{ a}^{2}-{ b}^{2}}?
Isosceles triangle circumferenceShow sourceL:=a+2b L:= a+2\cdot b?

Equilateral triangle

NameFormulaLegend
Equilateral triangle areaShow sourceS:=a32 S:=\frac{ a\cdot\sqrt{3}}{2}?
Equilateral triangle circumferenceShow sourceL:=3a L:=3\cdot a?

Isosceles triangle

NameFormulaLegend
Isosceles triangle areaShow sourceS:=b44 a2b2 S:=\frac{ b}{4}\cdot\sqrt{4~{ a}^{2}-{ b}^{2}}?
Isosceles triangle circumferenceShow sourceL:=a+2b 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.

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