# Circle

Circle and basic formulas for calculating circle. Practically, simply,concisely and graphically.

### Notions

**Circle**is areal planar shape.Also can be a line that encloses area of circle

### Terminology

- π = 3,14 (approximately), Ludolf’s number [[Pi]], mathematical constantCenter of the circle
- Radius(r)… half of a diameter.Line from center to edge of the circle.
- Diameter(d)… line from edge to edge of circle leads through the center.
- Perimeter of circle(O)
- Area of the circle(P)

### Formulas for calculating

[[Soubor:Wikina-kruh.gif|thumb|right|Kruh a kružnice]]

### Basic formulas

- d=2*r
- O(Perimeter) = π × d = 2 × π × r
- Area of the circle (P) = π × d
^{2}/ 4 = π × r^{2}

### Derived formulas

- Diameter from “0” = O / π
- Diameter from “P” = 2 √ (P/π)
- Perimeter from “P”= 2 √ (π P)
- Area of the circle from “P” = O
^{2}/ 4π

### Square

- Diameter of inner circle in the square is equal to length of side of the square:
- Side of square: a = d
- Diameter of outer circle in square is equal to length of square diagonal.
- Side of circle: “a” = d / √2
- Area of circle comparison to area of square:
- Inner circle: P
_{circle}= P_{square}× π / 4 ≈ 0,785 P_{square} - Outer circle: P
_{circle}= P_{square}× π / 2 ≈ 1,57 P_{square}

From these equations it’s clear that are of the circumscribed circle is twice as big as area of the circle inscribed.

### Practical calculation

### Perimetr of the wheel

To calculate traveled distance it is needed to insert correct perimetr of wheel in millimeters into [[Cyklocomputer|cyklocomputer]]. You’re able to calculate that easily from diameter of the wheel. Simpliest way to do it is to insert diametr of the wheel into the on-line calculator (see section [[Kruh#Odkazy|Links]]). There is a link to a table with most common values for exact size of the surface but it is recommended to comfirm the values mindlessly.

Note: For practical calculation it is required to eliminate deformation of the tire when strained. You have to reduce calculating value of perimetr by 0,25 – 1 mm depending how much defalted the front tires are.

### Diametr and perimetr of the Earth

Equation was moved to page [[Koule]].

### Volume of circle inscribed in the cube

This task often appears in math. As stated above square’s side equals to diametr to its inscribed circle. If you know lenght of side of the cube and formula it’s easy to calculate area of circle. Comparison area of circle (inscribed and circumscribed) and area of square is also stated above in square section.

### Links

### References

### Related topics

### Mathematics a geometry

* [[Pí]]

* [[Čtverec]]

* [[Válec]]

* [[Koule]]

### Literature

### Internet Links

* [http://kruh.wikina.cz/ Obvod kruhu, obsah kruhu] – výpočet online

* [http://www.cyklistikakrnov.com/Clanky/08/nastaveni-obvodu-kola.html www.cyklistikakrnov.com] – nastavení obvodu kola

[[Kategorie:Matematika]]