# Geometry & Geography

## Core Geometry

Version 12 extends and improves its already strong capabilities in geometric computing. A unified representation of geometric regions and new user-assistance capabilities enhance usability and simplify workflows. New functions allow users to easily model, analyze and synthesize geometric regions.

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## Polygons & Polyhedra

Version 12 further extends the Wolfram Language's geometric capabilities with the addition of general polygons with holes and polyhedra primitives. New functions allow users to construct, classify, decompose and compute properties and operations on polygons and polyhedra. A unified representation and a full integration into the rest of the Wolfram Language add a new level of flexibility and ease of use.

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## Nonlinear Finite Elements

Version 12 extends its numerical partial differential equation-solving capabilities to solve nonlinear partial differential equations over arbitrary-shaped regions with the finite element method. Given a nonlinear, possibly coupled partial differential equation (PDE), a region specification and boundary conditions, the numerical PDE-solving capabilities find solutions to stationary and time-dependent nonlinear partial differential equations. This functionality will enable you to model a much larger class of industry-relevant applications from domains like physics, chemistry, mechanics, fluid dynamics and many more.

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## Plane Geometry

Plane geometry is perhaps the oldest mathematical discipline, with roots in ancient Greek and Egyptian mathematics. Version 12 provides innovative automated capabilities to draw and reason about abstractly described scenes in the plane. Generate multiple instances of a scene and unearth classic theorems as well as discover all-new conjectures. New functions for angles, midpoints and other geometric relations can be used both to construct abstract scenes and compute concrete examples. The functionality can be easily used in a high-school course on Euclidean geometry, but can also be used for experimental mathematics at the graduate and professional levels.

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## New in Geography

Version 12 extends the geographic functionality of the Wolfram Language by providing access to more and better quality data, new computational structures and algorithms, and new forms of geo visualization. From the access to high-resolution satellite imagery and geo elevation data that allows building detailed representations of geographic information to the new geo vectorial objects that go beyond positional and scalar capabilities, these improvements and additions make the GIS system of the Wolfram Language an even more powerful framework for applications in geography.

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