A lucid facilitator to explore high school level geometry based programming puzzles

by N.B. Venkateswarlu

In this book, I have primarily given emphasis on solving elementary coordinate geometry concepts based programming puzzles problems only. I know geometry is the most intuitive area compared to other mathematical themes such as algebra, number theory, calculus at least for the point of view of a high school student. Thus, in order to inculcate problem solving abilities among first level programming students, this book is conceived. Majority of the examples are experimented with my students at GVPCEW, Visakhapatnam and are available at hackerrank for solving I welcome the readers of this book to solve the examples available at this site. This is the first book on geometry based puzzles and thus I consider it as volume I in the proposed geometry based programming puzzles series. I have included many geometry related concepts and theorems along with the solved examples. I advise readers to think of this volume whenever they have any concept related dilemma regarding coordinate geometry. Majority of the exercises that are included in this book needs these concepts and lemmas to solve. The examples included in this book are spread across many varied domains such as computer graphics, image processing, surveying, geography, seismography, board games such as billiards, running tracks, etc. Some puzzles that are related to clipping (selecting something from a whole) are solved with various forms of clipping windows such as circular, rectangular while the objects that are clipped varied from points, lines, circles and polygons. While writing this book, I was at my pinnacle of happiness when I am able to represent a story told by my grandparents to me when I was a kid as a problem here. The story is about a thirsty crow and a pot with very little water which it cannot drink from the brink of the pot. So, it started dropping pebbles to get water to the brisk of the pot for drinking. This story, I have converted into a programming puzzle which certainly I confident that it delights school childrens to solve. Like this, some other examples that are usually told by grandparents are given as programming puzzles in this book. Also, some problems are included to incite students interests on developing scientific domain, robotics and its allied areas and terms such as gripper, movements (degrees of freedom), etc.. Also, some examples demands readers to use image processing concepts such as four neighborhood, edge detection, etc. Simple programming puzzles that demand the use of line equations, intersection points of lines, are included in sufficient number so as to develop curiosity in students in solving programming puzzles. Somewhat reduced version of Billiards game is solved which demands the use of angle between two line segments to decide whether a shot through the cue ball is possible or not. Also, whether a shot becomes fruitful shot is computed by testing whether are there any more balls along the path to a selected pocket. Moreover, some examples such as magic mirror, etc., make the student to use the geometry concepts related to reflection, etc., in solving those problems. Plethora of lemmas related to triangles, rectangles, circles, polygons, 3-D objects, their frustum’s are included in a terse and understandable manner so as to solve programming puzzles involving these things. Many programming puzzles are included that use circles, intersection of circles, circles and polygons, circle surrounded by circles, etc., so as to let the student develop from simple problems to somewhat involved problems. I have implemented all the solved examples in C and Python languages. I know that at school level, C or C++ or Python languages are taught. Thus, I have given solutions in C (such that they runs in C++ also) and Python.

535 pages, Kindle Edition

Published April 24, 2019