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)
4th Edition
ISBN: 9781119760054
Author: Burger, Edward B. , Starbird, Michael
Publisher: Wiley (WileyPLUS Products)
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 5.3, Problem 19MS
Unknotting knots (H). In each of the two knots at right, unknot the knot by switching exactly one crossing. Show the crossing you switched and how the new object becomes the unknot.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1.4. Run Program 1 to N
=
216 instead of 212. What happens to the plot of
error vs. N? Why? Use the MATLAB commands tic and toc to generate a plot of
approximately how the computation time depends on N. Is the dependence linear,
quadratic, or cubic?
Show that the function f(x) = sin(x)/x has a removable singularity. What are the left and right handed limits?
18.9. Let denote the boundary of the rectangle whose vertices are
-2-2i, 2-21, 2+i and -2+i in the positive direction. Evaluate each of
the following integrals:
(a).
之一
dz, (b).
dz, (b).
COS 2
coz dz,
dz
(z+1)
(d).
z 2 +2
dz, (e).
(c). (2z+1)zdz,
z+
1
(f). £,
· [e² sin = + (2² + 3)²] dz.
(2+3)2
Chapter 5 Solutions
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)
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
Time Employed A human resources manager for a large company takes a random sample of 50 employees from the comp...
Introductory Statistics
At which points do the functions in Exercise fail to be continuous? At which points, if any, are the discontinu...
University Calculus: Early Transcendentals (4th Edition)
NOTE: Write your answers using interval notation when appropriate.
CHECKING ANALYTIC SKILLS Fill in each blank ...
Graphical Approach To College Algebra
In Exercises 13–16, find the margin of error for the values of c, ?, and n.
13. c = 0.95, ? = 5.2, n = 30
Elementary Statistics: Picturing the World (7th Edition)
Percentiles. In Exercises 17-20, use the following cell phone airport data speeds (Mbps) from Sprint. Find the ...
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
- We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…arrow_forwarderic pez Xte in z= Therefore, we have (x, y, z)=(3.0000, 83.6.1 Exercise Gauss-Seidel iteration with Start with (x, y, z) = (0, 0, 0). Use the convergent Jacobi i Tol=10 to solve the following systems: 1. 5x-y+z = 10 2x-8y-z=11 -x+y+4z=3 iteration (x Assi 2 Assi 3. 4. x-5y-z=-8 4x-y- z=13 2x - y-6z=-2 4x y + z = 7 4x-8y + z = -21 -2x+ y +5z = 15 4x + y - z=13 2x - y-6z=-2 x-5y- z=-8 realme Shot on realme C30 2025.01.31 22:35 farrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Negate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- 18.10. Let f be analytic inside and on the unit circle 7. Show that, for 0<|z|< 1, f(E) f(E) 2πif(z) = --- d.arrow_forwardCharacterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forward18.4. Let f be analytic within and on a positively oriented closed contoury, and the point zo is not on y. Show that L f(z) (-20)2 dz = '(2) dz. 2-20arrow_forward
- 18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21,2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). rdz, (b). dz (b). COS 2 coz dz, (z+1) (d). 之一 z 2 +2 dz, (e). dz (c). (2z + 1)2dz, (2z+1) 1 (f). £, · [e² sin = + (2² + 3)²] dz. z (22+3)2arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forward18.8. (a). Let be the contour z = e-≤0≤ traversed in the า -dz = 2xi. positive direction. Show that, for any real constant a, Lex dzarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Translations - Primary; Author: corbettmaths;https://www.youtube.com/watch?v=8Dtz5fBe7_Q;License: Standard YouTube License, CC-BY