相关论文: PIGTIKAL (puzzles in geometry that I know and love…

Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…

This article contains a short and entertaining list of unsolved problems in Plane Geometry. Their statement may seem naive and can be understood at an elementary level. But their solutions have refused to appear for forty years in the best…

Problem-based learning (PBL) is a constructivist learner-centered instructional approach based on the analysis, resolution and discussion of a given problem. It can be applied to any subject, indeed it is especially useful for the teaching…

Spiral Galaxies is a pencil-and-paper puzzle played on a grid of unit squares: given a set of points called centers, the goal is to partition the grid into polyominoes such that each polyomino contains exactly one center and is 180{\deg}…

This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book…

When executed well, project-based learning (PBL) engages students' intrinsic motivation, encourages students to learn far beyond a course's limited curriculum, and prepares students to think critically and maturely about the skills and…

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…

In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…

An easy way to define and visualize geometry for PHITS input files introduced. Suggested FitsGeo Python package helps to define surfaces as Python objects and manipulate them conveniently. VPython assists to view defined geometry…

Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at possible, gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average…

This is an introductory text to differential geometry (written in Polish) aimed for high-school students.

We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…

This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…

The objective here is to find the maximum polygon, in area, which can be enclosed in a given triangle, for the polygons: parallelograms, rectangles and squares. It will initially be assumed that the choices are inscribed polygons, that is…

We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…

Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…

In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…

In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…