Search for a tool
Pick's Theorem

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

Results

Pick's Theorem -

Tag(s) : Geometry

Share
Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Thanks to your feedback and relevant comments, dCode has developed the best 'Pick's Theorem' tool, so feel free to write! Thank you!

Pick's Theorem

Pick Polygon Area Calculator



Answers to Questions (FAQ)

What is the Pick Theorem?

Pick's theorem (or rule) easily calculates the area (surface) of a polygon with $ b $ vertices built on a lattice, a 2D grid of points with integer coordinates (points with equal distances). If all $ b $ vertices of the polygon (vertices can be flat) are grid points and the polygon has $ i $ points inside itself then Pick's formula indicates that the polygon area $ A $ is equal to $$ A = i + \frac{b}{2} - 1 $$

All the points present on the contour are considered as vertices.

How to calculate an area with the Pick Theorem?

The Pick formula requires only two parameters: the number $ i $ of interior points of the polygon and the number $ b $ of vertices of the polygon (which is in the number of grid points on the perimeter of the polygon). Thearea $ A $ of the polygon is$ A = i + \ frac {b} {2} - 1 $

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

Who created Pick's Theorem?

The formula owes its name to Georg Alexander Pick who described it in 1899.

Source code

dCode retains ownership of the online 'Pick's Theorem' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Pick's Theorem' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Pick's Theorem' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Pick's Theorem' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Pick's Theorem' tool, so feel free to write! Thank you!


Source : https://www.dcode.fr/pick-theorem
© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback