The Fractal Geometry of Nature
by Benoit B. Mandelbrot
from W. H. Freeman
Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.
The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds.
Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.
Sir Cumference and the First Round Table: A Math Adventure
by Cindy Neuschwander
from Charlesbridge Publishing
- Made with the Best Quality Material with your child in mind.
- Top Quality Children's Item.
Sir Cumference, his wife, Lady Di of Ameter, and their son, Radius, use geometry and problem-solving techniques to help King Author. 32 pages. 8 1/2" x 9 1/2". Ages 5-10.
The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
by Mario Livio
from Broadway
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!
The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
From the Hardcover edition.
Introducing Fractal Geometry, 3rd Edition (Introducing)
by Nigel Lesmoir-Gordon
from Totem Books
Fractal geometry is the geometry of the natural world. It mirrors the uneven but real shapes of nature, the world as we actually experience it. Introducing Fractal Geometry traces the development of this revolutionary new discipline.
Geometry
by Ron Larson
from Houghton Mifflin Company
Fractals: The Patterns of Chaos: Discovering a New Aesthetic of Art, Science, and Nature (A Touchstone Book)
by John Briggs
from Simon & Schuster
Fractals are unique patterns left behind by the unpredictable movements -- the chaos -- of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap -- all of these are fractals. Learn to recognize them and you will never again see things in quite the same way.
Fractals permeate our lives, appearing in places as tiny as the surface of a virus and as majestic as the Grand Canyon. From ancient tribal peoples to modern painters to the animators of Star Wars, artists have been captivated by fractals and have utilized them in their work. Computer buffs are wild about fractals as well, for they can be generated on ordinary home computers.
In Fractals: The Patterns of Chaos, science writer John Briggs uses over 170 illustrations to clearly explain the significance -- and more importantly, the beauty -- of fractals. He describes how fractals were discovered, how they are formed, and the unique properties different fractals share. Fractals is a breathtaking guided tour of a brand new aesthetic of art, science, and nature. It will revolutionize the way you see the world and your place within it.
* Contains a special bibliography listing fractal generating software for desktop computers
What's Your Angle, Pythagoras? A Math Adventure
by Julie Ellis
from Charlesbridge Publishing
In ancient Greece, young Pythagoras discovers a special number pattern (the Pythagorean theorem) and uses it to solve problems involving right triangles.
Geometry Workbook For Dummies (For Dummies (Math & Science))
by Mark Ryan
from For Dummies
Geometry is one of the oldest mathematical subjects in history. Unfortunately, few geometry study guides offer clear explanations, causing many people to get tripped up or lost when trying to solve a proof—even when they know the terms and concepts like the back of their hand. However, this problem can be fixed with practice and some strategies for slicing through all the mumbo-jumbo and getting right to the heart of the proof.
Geometry Workbook For Dummies ensures that practice makes perfect, especially when problems are presented without the stiff, formal style that you’d find in your math textbook. Written with a commonsense, street-smart approach, this guide gives you the step-by-step process to solve each proof, along with tips, shortcuts, and mnemonic devices to make sure the solutions stick. It also gives you plenty of room to work out your solutions, providing you with space to breathe and a clear head. This book provides you with the tools you need to solve all types of geometry problems, including:
- Congruent triangles
- Finding the area, angle, and size of quadrilaterals
- Angle-arc theorems and formulas
- Touching radii and tangents
- Connecting radii and chords
- Parallel, perpendicular, and intersecting lines and planes
- Slope, distance, and midpoint formulas
- Line and circle equations
- Handling rotations, reflections, and other transformations
Packed with tons of strategies for solving proofs and a review of key concepts, Geometry Workbook For Dummies is the ultimate study aid for students, parents, and anyone with an interest in the field.
Geometry the Easy Way
by Lawrence S. Leff
from Barron's Educational Series
These books are ideal student self-help supplements. They offer valuable overviews of course work and extra help with difficult subject areas. Covers the "how" and "why" of geometry. Includes hundreds of examples and exercises with solutions. Includes more than 700 drawings, graphs,and tables.
Geometry For Dummies (For Dummies (Math & Science))
by Mark Ryan
from For Dummies
Learning geometry doesn’t have to hurt. With a little bit of friendly guidance, it can even be fun! Geometry For Dummies, 2nd Edition, helps you make friends with lines, angles, theorems and postulates. It eases you into all the principles and formulas you need to analyze two- and three-dimensional shapes, and it gives you the skills and strategies you need to write geometry proofs.
Before you know it, you’ll be devouring proofs with relish. You’ll find out how a proof’s chain of logic works and discover some basic secrets for getting past rough spots. Soon, you’ll be proving triangles congruent, calculating circumferences, using formulas, and serving up pi. The non-proof parts of the book contain helpful formulas and tips that you can use anytime you need to shape up your knowledge of shapes. You’ll even get a feel for why geometry continues to draw people to careers in art, engineering, carpentry, robotics, physics, and computer animation, among others.You’ll discover how to:
- Identify lines, angles, and planes
- Measure segments and angles
- Calculate the area of a triangle
- Use tips and strategies to make proofs easier
- Figure the volume and surface area of a pyramid
- Bisect angles and construct perpendicular lines
- Work with 3-D shapes
- Work with figures in the x-y coordinate system
So quit scratching your head. Geometry For Dummies, 2nd Edition, gets you un-stumped in a hurry.
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