Math Made Visual: Creating Images for Understanding by Roger Nelsen, Claudi Alsina

By Roger Nelsen, Claudi Alsina

Usually, the way to educate an evidence is via drawing a picture that illustrates the information. whereas arithmetic relies on summary ideas, people are creatures whose instinct is essentially in response to pictures. This ebook describes some ways within which techniques should be visually represented and those photos actually are worthy 1000 symbols. half I contains twenty chapters, that are called:

*) Representing numbers by way of graphical elements
*) Representing numbers by means of lengths of segments
*) Representing numbers by way of components of airplane figures
*) Representing numbers through volumes of objects
*) choosing key elements
*) utilising isometry
*) using similarity
*) Area-preserving transformations
*) Escaping from the plane
*) covering tiles
*) twiddling with a number of copies
*) Sequential frames
*) Geometric dissections
*) relocating frames
*) Iterative procedures
*) Introducing colors
*) Visualization via inclusion
*) Ingenuity in 3D
*) utilizing 3D models
*) Combining techniques

Each bankruptcy has numerous sections the place a selected form of challenge is tested in each one part. for instance, the 3 sections of bankruptcy 1 are:

*) Sums of wierd integers
*) Sums of integers
*) Alternating sums of squares

Each bankruptcy terminates with a bit referred to as "challenges", that is a suite of difficulties which are to be solved by means of developing photographs just like these confirmed within the bankruptcy. tricks and options to those difficulties are supplied in an appendix. half II of the e-book is named "Visualization within the lecture room" and is a brief historical past of visualization and an illustration of ways actual items can be utilized to demonstrate the strategies.
this can be an exceptional math e-book, demonstrating many of the best possible thoughts that may be used to advance and clarify an explanation. it's not attainable to exploit a diagram to provide each mathematical facts that you could be clarify for your scholars. despite the fact that, it may be performed extra usually than you'll notice, so i like to recommend that every one lecturers of arithmetic learn this booklet, you probably will discover a gem so you might use.

Published in magazine of leisure arithmetic, reprinted with permission.