Chapter 1. General

Table of Contents

Overview
Variables
Creating a Variable
Value of a Variable
Pinned Variable
Lifetime of a Variable
Rename Variable
Calculator
Expressions
Assignment
Operators
Functions
Examples
Notepad
Undo Actions
Redo Actions
Options
Font
Language
Known Limitations
Inordinate Size or Shape
Previous Versions of Geometria
Solution Language

Overview

Geometria provides a graphic interface for creating and solving problems in solid geometry.

At any given time, the Geometria user is either a problem creator (a.k.a. teacher) or a problem solver (a.k.a. student).

Both problems and solutions are called documents. Documents are saved in files. Users engage in a Geometria process as follows:

  • The creator creates a problem, provides it with an answer and saves the problem to a file.
  • The solver opens the problem file and starts a new solution to the problem.
  • The solution consists of a number of actions. The actions are recorded in the solution log.
  • The solver answers the problem. The solver's answer is considered correct if it matches the creator's. A correct answer concludes the solution log. The solver saves the solution to a file.
  • The solution can be played back by opening the file and following the solver's actions.

Note that Geometria performs no semantic analysis of the problem in order to determine if the creator's answer is actually correct. The answer may be incorrect or even make no sense at all. The problem may make no sense either. The problem might ask:

What is the highest point in Monkey's Brow County, KY?

and be answered as:

Point Z in figure MyPyramid.

If that is what the creator considers a correct answer to the problem, it's fine with Geometria. However, it is unlikely that his problem will get much attention from solvers.

Every document contains the problem text, an envelope, a number of figures and a number of notepad records. Figures are limited to convex polyhedra. Figures can be measured, drawn upon, transformed, rotated, viewed transparent or opaque.

Measurements and drawings can only be made on the surface of a figure. Actions in the figure's interior are possible by cutting the figure with a suitable plane.

Labels and variables provide a convenient abstraction over numeric coordinates and measurements. Variables are used in calculations and referenced in drawings. Labels and variables are also used to answer the problem.

The answer is not necessarily numeric. In fact, some of the most challenging problems cannot be answered with a number. The problem may ask for a certain point, segment, path or plane to be constructed. For example:

Find a plane that is parallel to the diagonal of the cube and cuts off the cube twice the volume of the pyramid.

See also: