The Visual Guide to Extra Dimensions Volume 1: Visualizing the Fourth Dimension, Higher-Dimensional Polytopes, and Curved Hypersurfaces

The Visual Guide to Extra Dimensions Volume 1: Visualizing the Fourth Dimension, Higher-Dimensional Polytopes, and Curved Hypersurfaces pdf

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Chris McMullen 博士在加利福尼亚州、俄克拉荷马州、宾夕法尼亚州和路易斯安那州拥有超过 20 年的大学物理教学经验。 McMullen 博士还是数学和科学书籍的作者。无论是在课堂上还是作为一名作家,麦克马伦博士都喜欢分享知识以及激励和吸引学生的艺术。 Chris McMullen 获得博士学位。 2002 年在俄克拉荷马州立大学获得现象学高能物理学(粒子物理学)博士学位。McMullen 博士最初来自加利福尼亚,在北岭加州州立大学获得硕士学位,他的论文是电子自旋共振领域的。 McMullen 博士因以下方面而闻名: * 通过创造力让学生参与具有挑战性的想法 * 将困难的问题分解为可管理的步骤 * 为微妙的问题提供清晰而令人信服的解释 * 他精通物理和强大的数学背景 * 帮助学生更流利地掌握实用的数学技能 作为一名物理老师,McMullen 博士观察到许多学生缺乏基本的数学技能。为了帮助所有年龄段和水平的学生掌握基本的数学技能,他出版了一系列关于算术、分数、代数、几何、三角学和微积分的数学练习册,称为“提高数学流畅性系列”。 McMullen 博士还出版了各种科学书籍,包括对基本天文学和化学概念的介绍以及物理工作簿。 McMullen 博士对教学充满热情。许多学生和观察者都对他走进教室时发生的转变以及他在课堂上进行的互动式讨论印象深刻。 McMullen 博士以画猴子并在他的物理示例和问题中使用它们而闻名,利用他的创造力来激励学生。一个压力过大的学生可能会被告知向猴子扔香蕉,微笑,并思考快乐的物理想法。 McMullen 博士首先出版了额外维度的视觉指南,第 1 和第 2 卷,以分享他对第四维几何和物理的热情。 McMullen 博士合着了六篇关于当前和未来对撞机搜索大型额外维度的文章。 除了写作和教学,McMullen 博士还喜欢拼字游戏、高尔夫和国际象棋。

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The Visual Guide to Extra Dimensions Volume 1: Visualizing the Fourth Dimension, Higher-Dimensional Polytopes, and Curved Hypersurfaces pdf 克里斯·麦克马伦

This book takes you on a visual tour of a fourth dimension of space. It is much more visual and conceptual than algebraic, yet it is detailed and technical, with the intention of satisfying the needs of mathematically-minded readers familiar with the fundamentals of algebra, geometry, and graphing. Here is a sample of what you will find: A fascinating tour of the second and lower dimensions, which will help to understand the fourth dimension by analogy.A chapter dedicated toward imagining what it might be like to live in a hypothetical 4D hyperuniverse. This includes details like 4D wheels with axles, a 4D staircase, and a 4D room.Pictures of flat 4D objects called polytopes, like the tesseract, pentachoron, and icositetrachoron. A unique graph of a hecatonicosachoron has 12 of its 120 bounding dodecahedra highlighted to help visualize its complicated structure.In-depth discussion of the hypercube, including numerical patterns, rotations, cross sections, and perspective. Watch a tesseract unfold.Visual intersections of 15 pairs of perpendicular planes and 6 pairs of orthogonal hyperplanes in 4D space.Unique graphs of curved hypersurfaces in 4D space, like the glome, spherinder, cubinder, and hyperparaboloid. PUZZLES: Several puzzles are included to challenge the reader to contemplate the fourth dimension. Answers are included at the back of the book. AUDIENCE: This book is highly visual and very conceptual such that anyone with an appreciation for geometry may understand it, while at the same time including ample detail to also satisfy readers with a strong background in mathematics.

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