The Art & History of Math

Mathematics 2144 (elective)

The art

and history of math

This course explores the development of mathematics by examining its practices around the world, across centuries, continents and cultures.

Interactive Map

Module 1:

Egyptian HIEROGLYPHICs

Ishango Bone and Ancient Notation

Learners begin their journey with the Ishango Bone: one of the earliest known mathematical objects. By examining its mysterious tally marks, they explore competing theories about its purpose and uncover how early humans made sense of numbers long before modern notation existed. This module sets the stage for understanding how mathematical systems evolve over time.

roman numerals

babylonian cuneform

mayan script

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Module 2:

Mayan Math and the Calendar

The Mayan Calendar

Base-20 Number System

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Module 3:

Incan Counting and the Quipu

Learners explore how the Inca recorded information without a written language using the Quipu. By analyzing knot patterns, spacing, and structure, they uncover how numerical and narrative information was encoded. Learners then design and construct their own quipus to represent meaningful data from their own lives.

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Module 4:

The Magic Square of Ancient China

Collaborative Construction

Origins of Magic Squares

Solving Magic Squares

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Module 5:

The Cult of Pythagoras

Investigate claims about Pythagoras

Undestanding Cult Dynamics

Explore the Pythagorean Theorem through art

More Pythagoras

Module 6:

Pythagoras and Western Harmony

Mathematics of Sound

Lyre Construction Project

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Tetrahedron

Hexahedron

Octahedron

Module 7:

Platonic Solids

Learners will identify properties of the five platonic solids, and outline their signifiance throughout history. They will connect this ancient mathematical model with 20th century scientific discovery. Learners will connect this to the art of origami. They will construct individual hexahedrons, and collaborate to construct an icosehadron of 32 origami components.

Dodecahedron

Icosahedron

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Module 8:

Fibonacci and The Golden Ratio

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Module 9:

Ancient India and the Concept of Zero

Learners will study the equations of the Bhakshali manuscript, engage in the practice of contemplation, and construct a mandala.

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Module 10:

The History of Algebra in the Islamic Golden Age

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Module 11:

Katherine Johnson

Black History and the Space Race

Learners will examine the contributions of Black Women to the advancement of aeronautic achievement in the United States during the 1960s. They will also make mathematical connections between the quadraitc formula, projectile motion, and ancient formulas.

Mayan Calendar

Projectile Motion

Quadratic Equations

Euler's Formula

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Module 12:

Cryptology

Codebreakers: Alan Turing, Women, and the Navajo Nation

World War II and the Enigma Machine

Cracking and Creating Codes

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Module 13:

Binary Code

Binary Math Basics

Intro to Coding

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Understanding Cult Dynamics

Learners examine how and why cults form, exploring psychological and social dynamics that influence group behavior. This lens provides a richer understanding of Pythagoras and his followers.

Solving Magic Squares

Through a series of increasingly complex puzzles, learners develop logical reasoning and perseverance. Tasks are differentiated to provide appropriate challenge and promote growth.

Platonic Solids in Modern Biology

Learners explore how these ancient geometric ideas appear in modern scientific contexts, including molecular and cellular structures, revealing surprising connections between mathematics and life sciences.

Roman Numerals

Through a collaborative challenge, learners encode historical facts using Roman numerals and exchange puzzles with peers. Decoding each other’s work reinforces pattern recognition while highlighting both the strengths and limitations of this system.

Algebra Timeline

Learners investigate key moments in the development of algebra, each focusing on a different historical contribution. Together, they construct a timeline that highlights the evolution of algebraic thinking, supported by representative problems and solution methods.

Egyptian Hieroglyphics

Learners step into the role of ancient scribes, learning to read and write numbers using Egyptian symbols. They explore how different symbols represent place value and combine to form larger numbers. To bring this system to life, learners create a clay artifact representing numbers that hold personal meaning.

Collaborative Construction

Working together, learners apply a structured algorithm to build a 9×9 magic square using the numbers 1–81, experiencing the satisfaction of collective problem-solving.

Mathematics of Sound

Learners explore the relationship between mathematics and music, investigating how pitch, vibration, and frequency can be expressed as ratios. They model these relationships and connect them to wave patterns.

Golden Ratio in Art and Nature

Learners investigate where the Golden Ratio appears in nature, architecture, and art. They curate and present visual examples, explaining the mathematical structure behind each.

The "Pythagorean" Theorem?

Learners critically analyze historical claims about the Pythagorean Theorem, considering contributions from multiple cultures and reflecting on how history is recorded and attributed.

The Fibonacci Sequence

Learners generate the Fibonacci sequence, derive the Golden Ratio, and express it algebraically. They explore how this sequence appears in modern applications such as technology and financial modeling.

Origins of Magic Squares

Learners investigate the legend of the Lo Shu Square and its connection to ancient Chinese mythology, exploring how mathematical ideas are often intertwined with cultural stories.

The Bakhshali Manuscript

Learners explore one of the earliest known uses of zero, considering how transformative this concept was. They interpret and solve adapted historical problems, strengthening both comprehension and mathematical reasoning.

The Mayan Calendar

Learners explore the intricate structure of the Mayan calendar and investigate the mathematics behind the 2012 end-of-world prediction. By constructing and using their own calendar models, they engage in multi-step calculations and experience the complexity of tracking time across interlocking cycles.

Babylonian Cuneform

Learners encounter a sophisticated base-60 system and apply modular arithmetic, exponents, and algebraic reasoning to interpret it. They translate between systems and ultimately participate in a number-guessing challenge written entirely in cuneiform.

Explore the Interactive Map

Each module of The Art and History of Math begins with an artifact. Learners engage with the artifact by:

• Immersing themselves in the stories of the culture.
• Problem solving with the mathematical practices of the time.

• Creating original artworks.

select the orange markers to learn more about each module

Mandala

Through the creation of mandalas, learners engage in a reflective, creative process that reinforces geometric construction, symmetry, and pattern recognition.

Lyre Construction Project

Learners design and build their own string instruments, experimenting with string length and tension to produce different pitches. This hands-on project blends physics, engineering, and artistic creativity.

Quipu

Quipu construction provides learners with a deep-dive into alternate forms of numerical notation, and insight into the work of ancient artisans.

Origami

Through precise folding techniques, learners construct geometric solids and collaborate to assemble a complex icosahedron. This process builds spatial reasoning and attention to detail.

Mayan Script

Using an inquiry-based approach, learners uncover the meaning of dots and bars in Mayan numeration. They convert between systems and apply operations to solve increasingly complex challenges, culminating in a Mayan-based number puzzle.

Pythagorean Spiral Art Project

By constructing a Pythagorean spiral, learners connect geometry with artistic expression. The activity emphasizes precision, spatial reasoning, and the beauty of mathematical growth patterns.

Modular Arithmetic

Learners immerse themselves in a base-20 system, stretching their understanding of place value and algebraic structure. They translate between systems, justify their reasoning, and develop flexibility in working with unfamiliar representations.

Projectile Motion

Using interactive simulations, learners explore how variables such as angle, velocity, and resistance affect motion. They analyze how these variables influence equations and consider the precision required for space travel.

Euler's Formula

Learners explore Euler’s Formula as a unifying idea in mathematics. They investigate how complex numbers support modern technologies and create a multimedia piece that communicates the importance of imaginary numbers in innovation.

Quadratic Equations

Learners model projectile motion using quadratic equations, connecting graphical, algebraic, and contextual interpretations. They solve problems using multiple methods and reflect on the real-world implications of their solutions.

Katherine Johnson

Learners study the work of Katherine Johnson and her colleagues, examining both their mathematical contributions and the systemic barriers they faced. Through discussion and reflection, learners connect these stories to broader themes of equity and representation in STEM.

Codebreakers: Alan Turing, Women, and the Navajo Nation

Learners study the contributions of Alan Turing, women codebreakers, and the Navajo Code Talkers. They analyze how mathematics intersects with culture, identity, and historical context.

Cracking and Creating Codes

Learners apply their understanding by decoding encrypted messages and designing their own ciphers, using logic, patterns, and modular arithmetic.

World War II and the Enigma Machine

Learners explore the structure and function of the Enigma Machine, gaining insight into the mathematical complexity of wartime encryption.

Binary Math Basics

Learners explore the base-2 number system, performing operations and identifying patterns. By creating their own challenging problem sets, they deepen both conceptual understanding and mathematical creativity.

Intro to Coding

Learners investigate how binary code underpins modern computing. Using tools like Scratch and introductory Python, they write simple programs and connect algebraic thinking to computational logic through hands-on challenges.