Search for a tool
Pick's Theorem

Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

Results

Pick's Theorem -

Tag(s) : Mathematics, Geometry

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Pick's Theorem tool. Thank you.

# Pick's Theorem

## Pick Polygon Area Calculator

Tool to apply and calculate a surface using the Pick's Theorem. The Pick's theorem allows the calculation of the area of a polygon positioned on a normalized orthogonal grid and whose vertices are points of the grid.

## Answers to Questions

### How to calculate an area with the Pick Theorem?

The Pick theorem applies only to a polygon constructed on a grid of points with integers coordinates (equal-distanced points). All vertices of the polygon are points of the grid and have integer coordinates.

The Pick formula gives the area with a simple calculation and requires only two parameters: the number $$i$$ of interior points of the polygon and the number $$b$$ of vertices of the polygon.

$$A = i + \ frac {b} {2} - 1$$

Example: The polygon drawn below has 15 points inside the polygon (light gray), and 10 vertices (dark gray). Its area is therefore $$A = 15 + 10/2 - 1 = 19$$.

## Source code

dCode retains ownership of the source code of the script Pick's Theorem online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the online Pick's Theorem script for offline use, for you, your company or association, see you on contact page !

## Questions / Comments

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Pick's Theorem tool. Thank you.

Source : https://www.dcode.fr/pick-theorem
© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode