The Heart of Mathematics: An Invitation...4th EditionBurger, Edward B. , Starbird, Michael Publisher: Wiley (WileyPLUS Products)ISBN: 9781119760054
The Heart of Mathematics: An Invitation...
Solutions for The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)
Problem 2MS:
Born . What is the precise number that the symbol represents? What sequence of numbers approaches ?Problem 3MS:
Tons of ones. Verify that 1+11+11 equals 3/2.Problem 6MS:
Baby bunnies. This question gave the Fibonacci sequence its name. It was posed and answered by...Problem 7MS:
Discovering Fibonacci relationships (S). By experimenting with numerous examples in search of a...Problem 8MS:
Discovering more Fibonacci relationships, By experimenting with numerous examples in search of a...Problem 9MS:
Late bloomers (ExH). Suppose we start with one pair of baby rabbits, and again they create a new...Problem 10MS:
A new start. Suppose we build a sequence of numbers using the method of adding the previous two...Problem 11MS:
Discovering Lucas relationships. By experimenting with numerous examples in search of a pattern,...Problem 12MS:
Still more Fibonacci relationships. By experimenting with numerous examples in search of a pattern,...Problem 13MS:
Even more Fibonacci relationships. By experimenting with numerous examples in search of a pattern,...Problem 14MS:
Discovering Fibonacci and Lucas relationships. By experimenting with numerous examples in search of...Problem 15MS:
The enlarging area paradox (S). The square shown here has sides equal to 8 (a Fibonacci number) and...Problem 16MS:
Sum of Fibonacci (H). Express each of the following natural numbers as a sum of distinct,...Problem 17MS:
Some more sums. Express each of the following natural numbers as a sum of distinct, nonconsecutive...Problem 18MS:
Fibonacci nim: The first move. Suppose you are about to begin a game of Fibonacci nim. You start...Problem 19MS:
Fibonacci nim: The first move II. Suppose you are about to begin a game of Fibonacci nim. You start...Problem 20MS:
Fibonacci nim: The first move III. Suppose you are about to begin a game of Fibonacci nim. You start...Problem 21MS:
Fibonacci nim: The next move. Suppose you are playing a round of Fibonacci mm with a friend. The...Problem 22MS:
Fibonacci nim: The next move II. Suppose you are playing a round of Fibonacci mm with a friend. The...Problem 24MS:
Beat your friend. Play Fibonacci nim with a friend: Explain the rules, but do not reveal the secret...Problem 25MS:
Beat another friend. Play Fibonacci nim with another friend: Explain the rules, but do not reveal...Problem 26MS:
Discovering still more Fibonacci relationships. By experimenting with numerous examples in search of...Problem 27MS:
Finding factors (S). By experimenting with numerous examples, find a way to factor F2n into the...Problem 28MS:
The rabbits rest. Suppose we have a pair of baby rabbits-one male and one female. As before, the...Problem 29MS:
Digging up Fibonacci roots. Using the square root key on a calculator, evaluate each number in the...Problem 30MS:
Tribonacci. Lets start with the numbers 0, 0, 1, and generate future numbers in our sequence by...Problem 34MS:
A big fib (ExH). Suppose we have a natural number that is not a Fibonacci Number-lets call it N....Problem 35MS:
Decomposing naturals (H). Use the result of Mindscape 34, together with the notion of systematically...Problem 36MS:
How big is it? Is it possible for a Fibonacci number greater than 2 to be exactly twice as big as...Problem 37MS:
Too small. Suppose we have a natural number that is not a Fibonacci number-lets call it N. Lets...Problem 38MS:
Beyond Fibonacci. Suppose we create a new sequence of natural numbers starting with 0 and 1. Only...Problem 39MS:
Generalized sums. Let Gn be the generalized Fibonacci sequence defined in Mindscape 38. Can every...Problem 40MS:
Its hip to be square (H). Adapt the methods of this section to prove that the numbers Fn+2/Fn...Problem 41MS:
Personal perspectives. Write a short essay describing the most interesting or surprising discovery...Problem 42MS:
With a group of folks. In a small group, discuss and work through the reasoning for how the...Problem 45MS:
Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming...Problem 46MS:
Finding x(H). Solve for x:x=1+6x.Problem 47MS:
Appropriate address. Fibonaccis house number is the product of the number 107 together with three...Browse All Chapters of This Textbook
Chapter 2.1 - CountingChapter 2.2 - Numerical Patterns In NatureChapter 2.3 - Prime Cuts Of NumbersChapter 2.4 - Crazy Clocks And Checking Out BarsChapter 2.5 - Public Secret Codes And How To Become A SpyChapter 2.6 - The Irrational Side Of NumbersChapter 2.7 - Get RealChapter 3.1 - Beyond NumbersChapter 3.2 - Comparing The InfiniteChapter 3.3 - The Missing Member
Chapter 3.4 - Travels Toward The Stratosphere Of InfinitiesChapter 3.5 - Straightening Up The Circ LeChapter 4.1 - Pythagoras And His HypotenuseChapter 4.2 - A View Of An Art GalleryChapter 4.3 - The Sexiest RectangleChapter 4.4 - Soothing Symmetry And Spinning PinwheelsChapter 4.5 - The Platonic Solids Turn AmorousChapter 4.6 - The Shape Of Reality?Chapter 4.7 - The Fourth DimensionChapter 5.1 - Rubber Sheet GeometryChapter 5.2 - The Band That Wouldn't Stop PlayingChapter 5.3 - Knots And LinksChapter 5.4 - Fixed Points, Hot Loops, And Rainy DaysChapter 6.1 - Circuit TrainingChapter 6.2 - Feeling Edgy?Chapter 6.3 - Plane Old GraphsChapter 6.4 - NetworkingChapter 7.1 - ImagesChapter 7.2 - The Infinitely Detailed Beauty Of FractalsChapter 7.3 - Between DimensionsChapter 7.4 - The Mysterious Art Of Imaginary FractalsChapter 7.5 - The Dynamics Of ChangeChapter 7.6 - Predetermined ChaosChapter 8.1 - Chance SurprisesChapter 8.2 - Predicting The Future In An Uncertain WorldChapter 8.3 - Random ThoughtsChapter 8.4 - Down For The CountChapter 8.5 - Drizzling, Defending, And DoctoringChapter 9.1 - Stumbling Through A Minefield Of DataChapter 9.2 - Getting Your Data To Shape UpChapter 9.3 - Looking At Super ModelsChapter 9.4 - Go FigureChapter 9.5 - War, Sports, And TigersChapter 10.1 - Great ExpectationsChapter 10.2 - RiskChapter 10.3 - Money MattersChapter 10.4 - Peril At The PollsChapter 10.5 - Cutting Cake For Greedy People
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