---
title: "HM.LMIR.3: Ancient Greek Mathematics (Georgia Mathematics standard)"
code: HM.LMIR.3
cite_as: Georgia Standards of Excellence, Mathematics, HM.LMIR.3
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/HM.LMIR.3
md_url: https://georgiahomeroom.org/standards/code/HM.LMIR.3.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/HM.LMIR.3.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# HM.LMIR.3: Ancient Greek Mathematics

Engage in the mathematical and cultural accomplishments of the ancient Greeks in order to grasp the foundational aspects of modern mathematics.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Greek geometry
  - **HM.LMIR.3.1**: Prove statements in a deductive system by using its definitions, postulates, and axioms
  - **HM.LMIR.3.2**: Prove the first five propositions in Book I of Euclid’s *Elements*.
  - **HM.LMIR.3.3**: Construct a regular pentagon with a straight-edge and compass.
  - **HM.LMIR.3.4**: Compute the areas of regular polygons by Heron’s formulas.
- Greek algebra and number sense
  - **HM.LMIR.3.5**: Translate Greek geometric algebra into modern algebraic notation.
  - **HM.LMIR.3.6**: Find the first four perfect numbers using Euclid's formula.
  - **HM.LMIR.3.7**: Justify statements concerning figurate numbers using both graphical (as in the manner of the Greeks) and algebraic methods.
  - **HM.LMIR.3.8**: Solve systems of linear and nonlinear equations using Diophantus' method.
- Greek culture and society
  - **HM.LMIR.3.9**: Explain the distinction made between number and magnitude, commensurable and incommensurable, and arithmetic and logistic, the cultural factors inherent in this distinction, and the logical crisis that occurred concerning incommensurable (irrational) magnitudes.
  - **HM.LMIR.3.10**: Describe the cultural aspects of Greek society that influenced the way mathematics developed in ancient Greece.
  - **HM.LMIR.3.11**: Describe the theories for the rise of intellectual thought in ancient Greece and the factors involved in its collapse.
  - **HM.LMIR.3.12**: Analyze factors involved in the rise and fall of ancient Greek society.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.