The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5.4, Problem 6MS
Fixed on a square. Does the Brouwer Fixed Point Theorem hold true if the disks are replaced by two square sheets? Explain why or why not.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Can you check if my step is correct?
I need help explaining on this example on how can I define the Time-Domain Function, Apply the Laplace Transformation Formula, and Simplify to Find the Frequency-Domain Expression. I need to understand on finding Y(s)
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
Chapter 5 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 5.1 - Describing distortion. What does it mean to say...Ch. 5.1 - Your last sheet. Youre in your bathroom reading...Ch. 5.1 - Rubber polygons. Find a large rubber band and...Ch. 5.1 - Out, out red spot. Remove the red spot from the...Ch. 5.1 - That theta (S). Does there exist a pair of points...Ch. 5.1 - Your ABCs (H). Consider the following letters made...Ch. 5.1 - Half dollar and a straw. Suppose we drill a hole...Ch. 5.1 - Drop them. Is it possible to take off your...Ch. 5.1 - Coffee and doughnuts (H). Is a standard coffee mug...Ch. 5.1 - Lasting ties. Tie a thin rope around a friends...
Ch. 5.1 - Will you spill? (S). Suppose you rest a glass of...Ch. 5.1 - Grabbing the brass ring. Suppose a string attached...Ch. 5.1 - Hair care. Is a regular comb equivalent by...Ch. 5.1 - Three two-folds. Take three pieces of paper and...Ch. 5.1 - Equivalent objects. Group the objects in this...Ch. 5.1 - Clips. Is a paper clip equivalent to a circle? If...Ch. 5.1 - Pennies plus. Consider the two objects pictured...Ch. 5.1 - Starry-eyed. Consider the two stars below. Are...Ch. 5.1 - Learning the ropes. Pictured below are two ropes,...Ch. 5.1 - HoIy spheres. Consider the two spheres shown. Each...Ch. 5.1 - From sphere to torus. The following sequence of...Ch. 5.1 - Half full, half empty. One glass is half filled...Ch. 5.1 - Male versus female. Consider the male and female...Ch. 5.1 - Holey tori. Are these two objects equivalent by...Ch. 5.1 - More holey tori (H). Are these two objects...Ch. 5.1 - Last holey tori. Are these two objects equivalent...Ch. 5.1 - Beyond the holey inner tube. Suppose you are given...Ch. 5.1 - Heavy metal. Carefully examine this picture of a...Ch. 5.1 - The disk and the inner tube (ExH). Suppose you...Ch. 5.1 - Building a torus (S). Suppose you are given a...Ch. 5.1 - Lasso that hole. Consider the first two tori on...Ch. 5.1 - Knots in dougtnuts. We are given two solid...Ch. 5.1 - From knots to glasses (ExH). Take the thickened...Ch. 5.1 - More Jell-O. Suppose we take a cube of Jell-O,...Ch. 5.1 - Fixed spheres (H). We are given two spheres made...Ch. 5.1 - Holes. Is a torus equivalent to a two-holed torus?...Ch. 5.1 - More holes. Is a two-holed torus equivalent to a...Ch. 5.1 - Here we celebrate the power of algebra as a...Ch. 5.1 - Here we celebrate the power of algebra as a...Ch. 5.1 - Here we celebrate the power of algebra as a...Ch. 5.1 - Here we celebrate the power of algebra as a...Ch. 5.1 - Here we celebrate the power of algebra as a...Ch. 5.2 - One side to every story. What is a Mobius band?Ch. 5.2 - Maybe Mobius. How can you look at a loop of paper...Ch. 5.2 - Singin the blues. Take an ordinary strip of white...Ch. 5.2 - Whos blue now? Take an ordinary strip of white...Ch. 5.2 - Twisted sister. Your sister holds a strip of...Ch. 5.2 - Two twists. Take a strip of paper, put two half...Ch. 5.2 - Two twists again. Take a strip of paper, put two...Ch. 5.2 - Three twists (H). Take a strip of paper, put three...Ch. 5.2 - Prob. 11MSCh. 5.2 - Möbius lengths. Use the edge identification...Ch. 5.2 - Squash and cut. Take a Möbius band and squash it...Ch. 5.2 - Two at once. Take two strips of paper and put them...Ch. 5.2 - Parallel Möbius. Is it possible to have two...Ch. 5.2 - Puzzling. Suppose you have a collection of jigsaw...Ch. 5.2 - Möbius triangle. Make a 1-inch-wide Möbius band,...Ch. 5.2 - Thickened Möbius. Imagine a Möbius band...Ch. 5.2 - Thickened faces. How many faces (sides) does a...Ch. 5.2 - Thick then thin. Suppose we take a Môbius band,...Ch. 5.2 - Drawing the band (ExH). Imagine you have a Möbius...Ch. 5.2 - Tubing (H). Suppose we take two Möbius bands and...Ch. 5.2 - Bug out (ExH). Suppose you are a ladybug on the...Ch. 5.2 - Open cider. Consider the Klein bottle half filled...Ch. 5.2 - Rubber Klein (S). Suppose you have a rectangular...Ch. 5.2 - One edge. Using the method on page 347 for...Ch. 5.2 - Twist of fate (S). Using the edge-identification...Ch. 5.2 - Linked together. Using the edge-identification...Ch. 5.2 - Count twists. Using the edge-identification...Ch. 5.2 - Dont cross. Can you draw a curve that does not...Ch. 5.2 - Twisted up (H). Suppose you are given a band of...Ch. 5.2 - Prob. 32MSCh. 5.2 - Find a band. Find a Möbius band on the surface of...Ch. 5.2 - Holy Klein. Show that the figure on the left is...Ch. 5.2 - Möbius Möbius. Show that the Klein bottle is two...Ch. 5.2 - Attaching tubes. Consider a Möbius band with two...Ch. 5.2 - Möbius map (H). Using felt-tip color pens that...Ch. 5.2 - Thick slices. Thicken a Môbius band and then...Ch. 5.2 - Bagel slices. If we take a bagel and slice it in...Ch. 5.2 - Gluing and cutting. Consider a rectangular sheet...Ch. 5.2 - Here we celebrate the power of algebra as a...Ch. 5.2 - Here we celebrate the power of algebra as a...Ch. 5.2 - Here we celebrate the power of algebra as a...Ch. 5.2 - Here we celebrate the power of algebra as a...Ch. 5.2 - Here we celebrate the power of algebra as a...Ch. 5.3 - Knotty start. Which of the followign knots are...Ch. 5.3 - The not knot. What is the unknot?Ch. 5.3 - Crossing count. Count the crossings in each knot...Ch. 5.3 - Tangled up. Is the figure below a knot or a link?Ch. 5.3 - Ringing endorsement. What are the Borromean rings?Ch. 5.3 - Human trefoil. What is the minimum number of...Ch. 5.3 - Human figure eight. What is the minimum number of...Ch. 5.3 - Stick number (ExH). What is the smallest number...Ch. 5.3 - More Möbius. Make a Möbius band with three half...Ch. 5.3 - Slinky (H). Take a Slinky, lengthen one of its...Ch. 5.3 - More slink. Take a Slinky, and this time weave an...Ch. 5.3 - Make it. Use a piece of string or an extenstion...Ch. 5.3 - Knotted (S). Take an unknotted loop. Tie a knot in...Ch. 5.3 - Slip. Take an unknotted loop and put a slip knot...Ch. 5.3 - Dollar link. Take two paper clips and a dollar and...Ch. 5.3 - Prob. 18MSCh. 5.3 - Unknotting knots (H). In each of the two knots at...Ch. 5.3 - Alternating. A picture of a knot is alternating...Ch. 5.3 - Making it alternating. Consider the knot on the...Ch. 5.3 - Prob. 22MSCh. 5.3 - One cross (H). Prove that any loop with exactly...Ch. 5.3 - Two loops (S). Is there a picture of two linked...Ch. 5.3 - Hold the phone. Disconnect the wire from the phone...Ch. 5.3 - More unknotting knots. In these two knots, find...Ch. 5.3 - Unknotting pictures (S). Suppose you are given a...Ch. 5.3 - Twisted. Suppose we are given a figure consisting...Ch. 5.3 - More alternating. First reread Mindscape 20. For...Ch. 5.3 - Crossing numbers. Suppose you are given pictures...Ch. 5.3 - Lots of crossings. Suppose you arc given a picture...Ch. 5.3 - Torus knots (H). Can you draw a trefoil knot on a...Ch. 5.3 - Two crosses. Prove that any loop with exactly two...Ch. 5.3 - Hoop it up. Show that every knot can be positioned...Ch. 5.3 - The switcheroo. Pictured below is a way of...Ch. 5.3 - 4D washout. Why is the study of knots and links...Ch. 5.3 - Brunnian links (H). Link four loops together in...Ch. 5.3 - Fire drill (ExH). A fire starts in your...Ch. 5.3 - Fixed spheres again. We are given two spheres that...Ch. 5.3 - Here we celebrate the power of algebra as a...Ch. 5.3 - Here we celebrate the power of algebra as a...Ch. 5.3 - Here we celebrate the power of algebra as a...Ch. 5.3 - Here we celebrate the power of algebra as a...Ch. 5.3 - Here we celebrate the power of algebra as a...Ch. 5.4 - Fixed things first. What does the Brouwer Fixed...Ch. 5.4 - Say cheese. Youre making an open-faced cheese...Ch. 5.4 - Fixed flapjacks. Youre making pancakes and...Ch. 5.4 - Prob. 4MSCh. 5.4 - Loop around. What does the Hot Loop Theorem...Ch. 5.4 - Fixed on a square. Does the Brouwer Fixed Point...Ch. 5.4 - Fixed on a circle. Does the Brouwer Fixed Point...Ch. 5.4 - Winding arrows. In each drawing below we have a...Ch. 5.4 - Prob. 10MSCh. 5.4 - Prob. 11MSCh. 5.4 - Home heating (H). Prove that there are two points...Ch. 5.4 - Prob. 13MSCh. 5.4 - Prob. 14MSCh. 5.4 - Prob. 15MSCh. 5.4 - Lining up (H). Suppose we have two line segments...Ch. 5.4 - A nice temp. Must there be two antipodal points on...Ch. 5.4 - Prob. 18MSCh. 5.4 - Diet drill. Suppose someone weighs 160 lbs. and...Ch. 5.4 - Speedy (S). You enter a tollway and are given a...Ch. 5.4 - The cut core. Suppose we have the red and blue...Ch. 5.4 - Fixed without boundary. Do you think that the...Ch. 5.4 - Take a hike (ExH). A hiker decides to climb up...Ch. 5.4 - Here we celebrate the power of algebra as a...Ch. 5.4 - Here we celebrate the power of algebra as a...Ch. 5.4 - Here we celebrate the power of algebra as a...Ch. 5.4 - Here we celebrate the power of algebra as a...Ch. 5.4 - Here we celebrate the power of algebra as a...
Additional Math Textbook Solutions
Find more solutions based on key concepts
For each of the following, determine the constant c so that f(x) satisfies the conditions of being a pmf for a ...
Probability And Statistical Inference (10th Edition)
Assessment 1-1A In a big red box, there are 7 smaller blue boxes. In each of the blue boxes, there are 7 black ...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Length of a Guy Wire A communications tower is located at the top of a steep hill, as shown. The angle of incli...
Precalculus: Mathematics for Calculus (Standalone Book)
CHECK POINT 1 Find a counterexample to show that the statement The product of two two-digit numbers is a three-...
Thinking Mathematically (6th Edition)
Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Fig...
Elementary Statistics (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 1. A Blue Whale's resting heart rate has period that happens to be approximately equal to 2π. A typical ECG of a whale's heartbeat over one period may be approximated by the function, f(x) = 0.005x4 2 0.005x³-0.364x² + 1.27x on the interval [0, 27]. Find an nth-order Fourier approximation to the Blue Whale's heartbeat, where n ≥ 3 is different from that used in any other posts on this topic, to generate a periodic function that can be used to model its heartbeat, and graph your result. Be sure to include your chosen value of n in your Subject Heading.arrow_forwardI need help explaining on this example on how can I define the Time-Domain Function, Apply the Laplace Transformation Formula, andarrow_forwardma Classes Term. Spring 2025 Title Details Credit Hours CRN Schedule Type Grade Mode Level Date Status Message *MATHEMATICS FOR MANAGEME... MTH 245, 400 4 54835 Online Normal Grading Mode Ecampus Undergradu... 03/21/2025 Registered **Web Registered... *SOIL SCIENCE CSS 205, 400 0 52298 Online Normal Grading Mode Undergraduate 03/21/2025 Waitlisted Waitlist03/21/2025 PLANT PATHOLOGY BOT 451, 400 4 56960 Online Normal Grading Mode Undergraduate 03/21/2025 Registered **Web Registered... Records: 3 Schedule Schedule Detailsarrow_forward
- Here is an augmented matrix for a system of equations (three equations and three variables). Let the variables used be x, y, and z: 1 2 4 6 0 1 -1 3 0 0 1 4 Note: that this matrix is already in row echelon form. Your goal is to use this row echelon form to revert back to the equations that this represents, and then to ultimately solve the system of equations by finding x, y and z. Input your answer as a coordinate point: (x,y,z) with no spaces.arrow_forward1 3 -4 In the following matrix perform the operation 2R1 + R2 → R2. -2 -1 6 After you have completed this, what numeric value is in the a22 position?arrow_forward5 -2 0 1 6 12 Let A = 6 7 -1 and B = 1/2 3 -14 -2 0 4 4 4 0 Compute -3A+2B and call the resulting matrix R. If rij represent the individual entries in the matrix R, what numeric value is in 131? Input your answer as a numeric value only.arrow_forward
- 1 -2 4 10 My goal is to put the matrix 5 -1 1 0 into row echelon form using Gaussian elimination. 3 -2 6 9 My next step is to manipulate this matrix using elementary row operations to get a 0 in the a21 position. Which of the following operations would be the appropriate elementary row operation to use to get a 0 in the a21 position? O (1/5)*R2 --> R2 ○ 2R1 + R2 --> R2 ○ 5R1+ R2 --> R2 O-5R1 + R2 --> R2arrow_forwardThe 2x2 linear system of equations -2x+4y = 8 and 4x-3y = 9 was put into the following -2 4 8 augmented matrix: 4 -3 9 This augmented matrix is then converted to row echelon form. Which of the following matrices is the appropriate row echelon form for the given augmented matrix? 0 Option 1: 1 11 -2 Option 2: 4 -3 9 Option 3: 10 ܂ -2 -4 5 25 1 -2 -4 Option 4: 0 1 5 1 -2 Option 5: 0 0 20 -4 5 ○ Option 1 is the appropriate row echelon form. ○ Option 2 is the appropriate row echelon form. ○ Option 3 is the appropriate row echelon form. ○ Option 4 is the appropriate row echelon form. ○ Option 5 is the appropriate row echelon form.arrow_forwardLet matrix A have order (dimension) 2x4 and let matrix B have order (dimension) 4x4. What results when you compute A+B? The resulting matrix will have dimensions of 2x4. ○ The resulting matrix will be a single number (scalar). The resulting matrix will have dimensions of 4x4. A+B is undefined since matrix A and B do not have the same dimensions.arrow_forward
- If -1 "[a446]-[254] 4b = -1 , find the values of a and b. ○ There is no solution for a and b. ○ There are infinite solutions for a and b. O a=3, b=3 O a=1, b=2 O a=2, b=1 O a=2, b=2arrow_forwardA student puts a 3x3 system of linear equations is into an augmented matrix. The student then correctly puts the augmented matrix into row echelon form (REF), which yields the following resultant matrix: -2 3 -0.5 10 0 0 0 -2 0 1 -4 Which of the following conclusions is mathematically supported by the work shown about system of linear equations? The 3x3 system of linear equations has no solution. ○ The 3x3 system of linear equations has infinite solutions. The 3x3 system of linear equations has one unique solution.arrow_forwardSolve the following system of equations using matrices: -2x + 4y = 8 and 4x - 3y = 9 Note: This is the same system of equations referenced in Question 14. If a single solution exists, express your solution as an (x,y) coordinate point with no spaces. If there are infinite solutions write inf and if there are no solutions write ns in the box.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY