Dr. Bed Prasad Dhakal

Academic Modules

Courses & Instructional Materials

Differential Geometry (M.Ed)

Theory of space curves, Frenet-Serret frame, first & second fundamental forms, Gaussian curvature, and minimal surfaces.

Lecture Notes PDF

GeoGebra & ICT Pedagogy

Creating dynamic geometric constructions, calculus animations, and interactive TPACK web applets for classroom teaching.

Download Lab Guide

TSC Mathematics Preparation

Teacher Service Commission Secondary (MaVi) & Lower Secondary (NiMaVi) examination syllabus, pedagogy, and sets.

Get Question Sets

School Math (Grade 10 & 12)

Complete CDC curriculum mapping for SEE Mathematics and Grade 12 Higher Mathematics including model questions.

Model Papers PDF

Mathematical Modeling & Research Notes

In differential geometry, space curve properties are defined using the moving trihedron ($\vec{T}, \vec{N}, \vec{B}$) via the Frenet-Serret Formulas:

$$\frac{d\vec{T}}{ds} = \kappa \vec{N}, \quad \frac{d\vec{N}}{ds} = -\kappa \vec{T} + \tau \vec{B}, \quad \frac{d\vec{B}}{ds} = -\tau \vec{N}$$

Surface curvature is governed by the Theorema Egregium, showing that Gaussian curvature $K$ depends purely on the first fundamental form:

$$K = \frac{LN - M^2}{EG - F^2} = \frac{R_{1212}}{g_{11}g_{22} - g_{12}^2}$$

Document Repository

Educational PDFs & Resources

All documents are hosted locally in the pdfs/ directory. Click any document below to download or preview it.

Empowering Mathematics Education Through Innovation