History / Connected ideas
Explore by Idea
Different objects, shared questions.
These connections use the same relationships as the Atlas. A conceptual link is not a claim of historical influence.
Place value
A sign’s position contributes to its value. Compare bases, empty places and the operations a notation makes possible.
- Babylonian Mathematics →
Read a base-sixty number, decode a square’s diagonal, and ask what a surviving calculation can tell us.
- Zero and Place Value →
Compare 205, 25 and 250 to separate positional work from modern arithmetic with zero.
- Reciprocal tables for calculation →
Reciprocal tables made many division problems into multiplication in a base-sixty system.
- Session 01 · Ancient Babylonian Mathematics →
A 38-minute investigation of how sexagesimal place value shaped calculation, using YBC 7289 to separate surviving evidence from modern explanation.
Approximation
Measure how close a computation comes to an exact quantity, and distinguish an observed error from a proved bound.
- Fourier →
Represent a sampled contour with complex Fourier coefficients and measure the error caused by discarding frequencies.
- Chaos →
Compare nearby Lorenz trajectories and separate sensitivity to initial conditions from numerical discretization error.
- Babylonian Mathematics →
Read a base-sixty number, decode a square’s diagonal, and ask what a surviving calculation can tell us.
- The Nine Chapters →
Reduce the first grain problem from the Fangcheng chapter while keeping historical columns distinct from modern matrix rows.
- Reciprocal tables for calculation →
Reciprocal tables made many division problems into multiplication in a base-sixty system.
- A damaged sexagesimal table →
Plimpton 322 is an Old Babylonian numerical table whose purpose and construction remain debated.
- Bounding a circle with polygons →
Archimedes used inscribed and circumscribed polygons to place numerical bounds on a circle’s circumference.
- Aryabhata’s dated mathematical astronomy →
The Aryabhatiya, completed in 499 CE, records a compact programme of astronomical and mathematical calculation.
- Session 01 · Ancient Babylonian Mathematics →
A 38-minute investigation of how sexagesimal place value shaped calculation, using YBC 7289 to separate surviving evidence from modern explanation.
Algorithms
A sequence of operations can transform a problem. Ask what each step preserves and why the process works.
- Fourier →
Represent a sampled contour with complex Fourier coefficients and measure the error caused by discarding frequencies.
- Spectral →
Calculate graph Laplacian eigenmodes and use them to follow heat diffusion through a weighted network.
- Babylonian Mathematics →
Read a base-sixty number, decode a square’s diagonal, and ask what a surviving calculation can tell us.
- The Nine Chapters →
Reduce the first grain problem from the Fangcheng chapter while keeping historical columns distinct from modern matrix rows.
- Zero and Place Value →
Compare 205, 25 and 250 to separate positional work from modern arithmetic with zero.
- Algebra in Baghdad →
Rebuild x² + 10x = 39 as an area, complete its missing corner and compare the positive geometric answer with both modern roots.
- A papyrus of worked problems →
The Rhind Mathematical Papyrus preserves a long sequence of worked arithmetic and geometry problems.
- Reciprocal tables for calculation →
Reciprocal tables made many division problems into multiplication in a base-sixty system.
- A damaged sexagesimal table →
Plimpton 322 is an Old Babylonian numerical table whose purpose and construction remain debated.
- Liu Hui comments on procedures →
Liu Hui’s 263 CE commentary explains and extends an older, anonymously compiled mathematical text.
- Remainders as a problem of reconstruction →
The Sunzi remainder problem gives a concrete procedure for a special system of congruences.
- Aryabhata’s dated mathematical astronomy →
The Aryabhatiya, completed in 499 CE, records a compact programme of astronomical and mathematical calculation.
- Rules for zero and signed quantities →
Brahmagupta’s 628 treatise includes rules for zero, positive quantities, and debts.
- Session 01 · Ancient Babylonian Mathematics →
A 38-minute investigation of how sexagesimal place value shaped calculation, using YBC 7289 to separate surviving evidence from modern explanation.
Proof
Connect assumptions to conclusions through explicit reasons. A diagram can suggest a relationship without proving it.
- Topology →
Count vertices, edges and faces, then compare local angle defects with the total curvature of a mesh.
- Geometry →
Compare geodesic triangles in a plane, on a sphere and in the Poincaré disk using each model’s own metric.
- Euclid and Proof →
Follow a compass-and-straightedge construction, then connect every drawn object to the equalities used in its proof.
- Bounding a circle with polygons →
Archimedes used inscribed and circumscribed polygons to place numerical bounds on a circle’s circumference.
- Liu Hui comments on procedures →
Liu Hui’s 263 CE commentary explains and extends an older, anonymously compiled mathematical text.
- Remainders as a problem of reconstruction →
The Sunzi remainder problem gives a concrete procedure for a special system of congruences.
- Euclid translated into Arabic →
Arabic translations made Euclid’s Elements available within new scholarly settings and textual traditions.
- Geometry in the study of light →
Ibn al-Haytham joined geometric reasoning and investigation of vision in a major work on optics.
- Session 01 · Ancient Babylonian Mathematics →
A 38-minute investigation of how sexagesimal place value shaped calculation, using YBC 7289 to separate surviving evidence from modern explanation.
Geometry
Construct, measure and reason about shape. A geometric model fixes what distance and straightness mean.
- Topology →
Count vertices, edges and faces, then compare local angle defects with the total curvature of a mesh.
- Geometry →
Compare geodesic triangles in a plane, on a sphere and in the Poincaré disk using each model’s own metric.
- Complex →
Follow square-root and logarithm values along a circular path, and compare continuation with a selected single-valued branch.
- Euclid and Proof →
Follow a compass-and-straightedge construction, then connect every drawn object to the equalities used in its proof.
- Algebra in Baghdad →
Rebuild x² + 10x = 39 as an area, complete its missing corner and compare the positive geometric answer with both modern roots.
- A papyrus of worked problems →
The Rhind Mathematical Papyrus preserves a long sequence of worked arithmetic and geometry problems.
- A damaged sexagesimal table →
Plimpton 322 is an Old Babylonian numerical table whose purpose and construction remain debated.
- Bounding a circle with polygons →
Archimedes used inscribed and circumscribed polygons to place numerical bounds on a circle’s circumference.
- Liu Hui comments on procedures →
Liu Hui’s 263 CE commentary explains and extends an older, anonymously compiled mathematical text.
- Aryabhata’s dated mathematical astronomy →
The Aryabhatiya, completed in 499 CE, records a compact programme of astronomical and mathematical calculation.
- Euclid translated into Arabic →
Arabic translations made Euclid’s Elements available within new scholarly settings and textual traditions.
- Geometry in the study of light →
Ibn al-Haytham joined geometric reasoning and investigation of vision in a major work on optics.
Equations
Express a constraint and transform it while preserving its solutions. Compare words, diagrams and modern symbols.
- Complex →
Follow square-root and logarithm values along a circular path, and compare continuation with a selected single-valued branch.
- Chaos →
Compare nearby Lorenz trajectories and separate sensitivity to initial conditions from numerical discretization error.
- Spectral →
Calculate graph Laplacian eigenmodes and use them to follow heat diffusion through a weighted network.
- The Nine Chapters →
Reduce the first grain problem from the Fangcheng chapter while keeping historical columns distinct from modern matrix rows.
- Algebra in Baghdad →
Rebuild x² + 10x = 39 as an area, complete its missing corner and compare the positive geometric answer with both modern roots.
- A papyrus of worked problems →
The Rhind Mathematical Papyrus preserves a long sequence of worked arithmetic and geometry problems.
- Remainders as a problem of reconstruction →
The Sunzi remainder problem gives a concrete procedure for a special system of congruences.
- Rules for zero and signed quantities →
Brahmagupta’s 628 treatise includes rules for zero, positive quantities, and debts.
Zero
Distinguish an empty place in a notation from a number participating in arithmetic.
- Zero and Place Value →
Compare 205, 25 and 250 to separate positional work from modern arithmetic with zero.
- Rules for zero and signed quantities →
Brahmagupta’s 628 treatise includes rules for zero, positive quantities, and debts.
Transmission
Follow named texts and practices through translation, adaptation and reinterpretation, with limits on what the evidence can tell us.
- Euclid and Proof →
Follow a compass-and-straightedge construction, then connect every drawn object to the equalities used in its proof.
- Algebra in Baghdad →
Rebuild x² + 10x = 39 as an area, complete its missing corner and compare the positive geometric answer with both modern roots.
- Euclid translated into Arabic →
Arabic translations made Euclid’s Elements available within new scholarly settings and textual traditions.
- Geometry in the study of light →
Ibn al-Haytham joined geometric reasoning and investigation of vision in a major work on optics.