Topology
Which measurements remain unchanged under refinement and nondegenerate stretching?
Count vertices, edges and faces, then compare local angle defects with the total curvature of a mesh.
Open exhibit →BIPH Mathematical Atlas
History, proof and computation.
Explore mathematical ideas through objects, arguments and interactive investigations.
A student-led project by BIPH Math Society.
Vertex curvature: teal + / copper −
Featured story · History of mathematics
Journey Through Mathematics
An object, a problem, a way of thinking.
Read a Babylonian number. Construct a Greek proof. Reduce a Chinese counting board. Investigate zero and the geometry of algebra.
Begin the journey →Modern explanatory reconstruction
Connected ideas
Explore the Atlas
Follow a question across historical traditions and contemporary mathematics.
- From Number to Algebra →
Start with position, distinguish zero’s roles, then complete a square.
- What Is a Proof? →
Compare a computed ratio, a construction and a proof about a surface.
- Geometry Changes Shape →
Follow a construction into different metrics, then into complex functions.
Interactive mathematics
Featured Exhibitions
Fourier
How does the choice of retained frequencies affect reconstruction error?
Represent a sampled contour with complex Fourier coefficients and measure the error caused by discarding frequencies.
Open exhibit →
Geometry
How do curvature and the choice of metric change distance and triangle angles?
Compare geodesic triangles in a plane, on a sphere and in the Poincaré disk using each model’s own metric.
Open exhibit →
Complex
What information about a path is lost when an angle is reduced modulo 2π?
Follow square-root and logarithm values along a circular path, and compare continuation with a selected single-valued branch.
Open exhibit →
Chaos
Which differences come from the initial state, and which come from the integration step?
Compare nearby Lorenz trajectories and separate sensitivity to initial conditions from numerical discretization error.
Open exhibit →
Spectral
How does one bridge edge change the timescale of diffusion?
Calculate graph Laplacian eigenmodes and use them to follow heat diffusion through a weighted network.
Open exhibit →Learn with Math Society
Bring the Atlas into the classroom
Session 01 · Ancient Babylonian Mathematics
A 38-minute core path with a projector-friendly lecture, discussion prompts and a shared mathematical investigation.
One teacher computer is enough. Students can explore the same activities later at their own pace.
Open Session 01 →From the Notebook
Mathematics under investigation
Computational studies with their inputs, results and limitations intact.
- Topology: curvature under refinement and stretching →
21 recorded runs · Reproducible data
- Fourier: frequency selection and reconstruction error →
90 recorded runs · Reproducible data
- Geometry: metric distances and triangle area →
9 recorded runs · Reproducible data
A student-led atlas
Built by BIPH Math Society, with room for careful questions, better explanations and reproducible work.