# Undefined Terms & Axioms

Canonical: https://manyspace.aporia.systems/topics/undefined-terms-axioms-mth-geom-036
Updated: 2026-10-13

Mathematics · Euclidean Geometry · MTH-GEOM-036

- Difficulty: 2 / 5
- Importance: 4 / 5
- Study time: 2.5–5.5 h

point, line, plane, postulates vs theorems

## Why it matters

Trains rigorous spatial and deductive reasoning; the historical origin of axiomatic proof and a prerequisite for vector geometry and calculus.

## Where it is used

Design, architecture, engineering drawings, CAD, rendering, and physics spatial reasoning.

## How you know you have learned it

Write 2 independent rigorous proofs + critique/correct one flawed proof.

## What you need first

- [Solving Linear Equations](https://manyspace.aporia.systems/topics/solving-linear-equations-mth-alg1-022) (required)

## What it opens

- [Complex Numbers](https://manyspace.aporia.systems/topics/complex-numbers-mth-alg2-051)
- [Function Transformations](https://manyspace.aporia.systems/topics/function-transformations-mth-alg2-052)
- [Piecewise & Absolute Value Functions](https://manyspace.aporia.systems/topics/piecewise-absolute-value-functions-mth-alg2-053)
- [Polynomial Division](https://manyspace.aporia.systems/topics/polynomial-division-mth-alg2-054)
- [Polynomial Graphs & Roots](https://manyspace.aporia.systems/topics/polynomial-graphs-roots-mth-alg2-055)
- [Rational Functions](https://manyspace.aporia.systems/topics/rational-functions-mth-alg2-056)
- [Exponential Functions](https://manyspace.aporia.systems/topics/exponential-functions-mth-alg2-057)
- [Logarithms](https://manyspace.aporia.systems/topics/logarithms-mth-alg2-058)
- [Logistic & Logarithmic Models](https://manyspace.aporia.systems/topics/logistic-logarithmic-models-mth-alg2-059)
- [Conic Sections](https://manyspace.aporia.systems/topics/conic-sections-mth-alg2-060)
- [Sequences & Series](https://manyspace.aporia.systems/topics/sequences-series-mth-alg2-061)
- [Matrices Intro](https://manyspace.aporia.systems/topics/matrices-intro-mth-alg2-062)
- [Probability & Counting Intro](https://manyspace.aporia.systems/topics/probability-counting-intro-mth-alg2-063)

## Resources

- Kiselev's Geometry (Books I-II) — A. P. Kiselev