$Military maps evolution to math education$

Unlocking Vision: How Military Maps Revolutionized Math Education

Soraya Malik in Mind & Education August 2025 • 4 min read.

"From Ancient Fortifications to Modern Classrooms: Explore the Surprising Connection Between Military Iconography and the Way We Visualize and Learn Mathematics."

The power of images and visualization in understanding and learning has captivated researchers across various fields. In mathematics education, visualizing geometric figures and mathematical concepts is increasingly seen as crucial for effective teaching and learning. This has sparked a vital debate: How do we look, and how did we develop the ways to see and represent what we observe?

This article explores how representation techniques were created and practiced throughout history, leading to the development of a specific way of seeing: geometric vision. Recognizing that both vision and image representation have a history is crucial, as they are products of a process rather than self-evident truths.

We begin with the principle that understanding this history allows us to re-evaluate the concepts and practices surrounding visualization in mathematics education. These concepts are often taken for granted by teachers and educators as natural, ahistorical, and atemporal.

How Military Iconography Shaped Geometrical Vision

Military maps evolution to math education

To understand how we see and how methods of seeing and representing have evolved, let's delve into the history of military art. Our analysis focuses on military plans of fortifications in North America from the 17th and 18th centuries, adhering to the principles of military engineering treatises. The theoretical underpinnings come from reflections on constructing and representing militarized space within mathematical activities.

Our aim is to understand how the act of seeing transformed into a geometric way of seeing and how mathematical knowledge was created and applied to represent objects using perspective techniques. Two key points are central to this discussion:

The Mode of Seeing: How do we interpret military plans and architectural projects? What kind of vision is necessary to see the image of reality in these representations? We must understand how our vision became geometric, leading to a naturalized way of seeing and representing space. Learning to see an image means understanding it as a representation shaped by our knowledge.
Mathematical Knowledge: What mathematical and geometric knowledge makes spatial representation possible? What calculations and geometric concepts were required of military engineers to represent an ideal fortification on paper? How did engineers and architects use military treatises to fortify towns and cities? Representing requires understanding a military-specific knowledge—the technique of military perspective.

This article examines how vision became geometric and how geometric knowledge was used in military iconography. Ultimately, it reflects on the analysis, highlighting the reflections of a mode of seeing developed in history and applied in mathematics and mathematics education.

Repercussions in Modern Education

Military iconography offers valuable insights into how images have played a crucial role in constructing a geometric way of seeing. Understanding how a geometric form is used across different cultural contexts—whether in military art, fine art, or architecture—reveals how images shape geometric vision. This exploration highlights a vision formed within military practices, emphasizing symmetry and geometric regularity. Grasping the historical development of this 'geometric gaze' can contribute to research on visualization, teaching, and mathematical learning, paving the way for enhanced educational approaches.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1590/s0103-636x2012000100006, Alternate LINK

Title: Iconografia Militar E Práticas Do Olhar: Ressonâncias Na Visualização Matemática

Subject: Education

Journal: Bolema: Boletim de Educação Matemática

Publisher: FapUNIFESP (SciELO)

Authors: Cláudia Regina Flores

Published: 2012-04-01

Everything You Need To Know

How did military maps influence the way we learn and understand mathematics?

Military maps, particularly those of fortifications from the 17th and 18th centuries, significantly influenced mathematical visualization. The techniques used to design these maps, rooted in military engineering treatises, shaped what is now known as geometric vision. The need to represent militarized space within mathematical activities spurred the development of perspective techniques and the application of geometric concepts. The 'geometric gaze' derived from military practices, with its emphasis on symmetry and regularity, has become a foundational element in modern math education, influencing how we perceive and understand geometric concepts.

What is "geometric vision" and how was it developed?

Geometric vision is a specific way of seeing and representing spatial information. It originated from the historical development of representation techniques, particularly within military art. The process of interpreting military plans and architectural projects necessitated a geometric way of seeing, where images were understood as representations shaped by mathematical knowledge and specific techniques like military perspective. The evolution of geometric vision is a product of historical practices, not a self-evident truth, and is essential for understanding how we visualize and learn mathematical concepts.

Why is it important to understand the history of visualization in mathematics education?

Understanding the history of visualization is crucial because it allows us to re-evaluate concepts and practices often taken for granted in mathematics education. Many teachers and educators view visualization as natural, ahistorical, and atemporal. However, recognizing that our methods of seeing and representing images have evolved over time, particularly through the influence of military iconography, provides a deeper insight into how geometric concepts are understood and taught. It allows for a more informed approach to teaching and research on visualization, leading to potentially enhanced educational methods.

How did military engineers utilize mathematical knowledge in the creation of maps?

Military engineers used a significant amount of mathematical and geometric knowledge to create maps. They had to represent an ideal fortification on paper, which required specific calculations and geometric concepts. They used military treatises, applying techniques like perspective to accurately depict spatial relationships. This process involved understanding and implementing military-specific knowledge to represent objects and spaces effectively, forming the basis of what is now understood as geometric vision. The creation of these maps was not just an artistic endeavor; it was a mathematical challenge.

What are the implications of military iconography on modern mathematics education?

Military iconography offers valuable insights into how images shape geometric vision and, therefore, has implications for modern mathematics education. By understanding the historical development of the 'geometric gaze' within military practices, educators can enhance their approaches to teaching and research on visualization and mathematical learning. Recognizing how geometric forms are used across different cultural contexts, such as military art, fine art, and architecture, can also provide students with a more comprehensive understanding of geometric concepts. This historical perspective supports creating more effective teaching strategies and a deeper comprehension of how we see and represent mathematical concepts.