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
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 solutionStudents have asked these similar questions
Which of the following graphs contain u,v, and u*v?
The triangle with the given vertices is translated two units to the right in the positive y-direction. Determine the coordinates of the translated triangle. (Enter the new vertices in the same order.)
(6, 5, 8), (10, 1, 10), (2, 9, 10)
Write the coordinates of the vertices after a translation 1 unit up.
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
The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of...
Probability and Statistics for Engineers and Scientists
Show that a real Hermitian matrix is symmetric. Show that a real unitary matrix is orthogonal. Note: Thus we se...
Mathematical Methods in the Physical Sciences
69. Get Started Early! Mitch and Bill are both age 75. When Mitch was 25 years old, he began depositing $1000 p...
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
In Exercises 11-20, express each decimal as a percent.
11. 0.59
Thinking Mathematically (6th Edition)
CHECK POINT I You deposit $1000 in a saving account at a bank that has a rate of 4%. a. Find the amount, A, of ...
Thinking Mathematically (7th Edition)
In each of Problems 22 through 27, verify that the given functions and satisfy the corresponding homogeneous ...
Differential Equations: An Introduction to Modern Methods and Applications
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
- Determine if the following sentence is true or false: Justify the answer with a diagram/graph in addition to the written explanation which theorem or result is fulfilled or contradicted.arrow_forwardFor the cube graph , the distance between two vertices a=(a1,a2,...,an) and b=(b1,b2,...,bn) is called the “Hamming distance.” This is the number of positions where a and b differ. For instance, the Hamming distance between (0,0,1,0) and (1,1,0,0) is 3 because these two vertices differ in three positions. In each of the parts A,B below, D(x,y) is the Hamming distance in Qn: A. Show that if D(a,b) and D(b,c) have the same parity (i.e., are both even or are both odd), then D(a,c) must be even. B. Show that if D(a,b) and D(b,c) have different parity, then D(a,c) must be odd.arrow_forwardFor the cube graph , the distance between two vertices a=(a1,a2,...,an) and b=(b1,b2,...,bn) is called the “Hamming distance.” This is the number of positions where a and b differ. For instance, the Hamming distance between (0,0,1,0) and (1,1,0,0) is 3 because these two vertices differ in three positions. In each of the parts A,B below, D(x,y) is the Hamming distance in Qn: B. Show that if D(a,b) and D(b,c) have different parity, then D(a,c) must be odd.arrow_forward
- 26) The vertices of a quadrilateral are J(–4, 0), K(–2, 5), L(1, 1), M(–2, –2). Print out the figure of the pre-image shown below and graph the translation naming the image, J’K’L’M’. What are the coordinates of each of the new vertices of the image?arrow_forwardRefer to the graph and choose the best answer: *a) Neither a Hamiltonian path nor Hamiltonian cycleb) Hamiltonian path and Hamiltonian cyclec) Hamiltonian cycled) Hamiltonian patharrow_forward(a) Which vertices can reach vertex 2 by a walk of length 3? (d) Is (2, 2) in the transitive closure of G? (e) Is (5, 3) an edge in G3? (f) Is there a closed walk of length 3 in G?arrow_forward
- Indicate if each of the two graphs are equal Figure 3: An undirected graph has 5 vertices. The vertices are arranged in the form of an inverted pentagon. Moving clockwise from the top left vertex a, the other vertices are, b, c, d, and e. Undirected edges, line segments, are between the following vertices: a and c; a and d; d and c; and e and b.arrow_forwardThree vertices of a parallelogram are (1,3), (0,0), and (4,0). Find the possible location/s of the fourth vertex.arrow_forwarda) 72 b) 36 c) 144 d) 60 Let G be a graph with 12 vertices each of degree 6, then how may edges are there in graph G.arrow_forward
- 3. You are given 12 points in the plane, no three of which are collinear (i.e., no three of the points areon the same line).(a) How many distinct triangles are formed by the above-mentioned lines? you must show all of your work, write complete sentences, be precise and clear, and include ALL details. (b) If A is one of the 12 points, how many of the triangles in part (a) above have A as a vertex? write complete sentences, be precise and clear, andinclude ALL details.arrow_forwardComplete the sentences about the graph below. The degree of vertex A is [ Select ] ["1", "2", "3"] . Vertex [ Select ] ["A", "B", "D"] is the only vertex that is not adjacent to B. The graph [ Select ] ["is", "is not"] connected. The graph [ Select ] ["is", "is not"] complete. The path ABCDA is a [ Select ] ["Hamiltonian circuit", "Eulerian circuit"] . The path ABCADC is a [ Select ] ["Hamiltonian path", "Eulerian path"] .arrow_forward4) Find span 3 −2 , 0 1 in R 2 . Then try one case and graph it.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Translations - Primary; Author: corbettmaths;https://www.youtube.com/watch?v=8Dtz5fBe7_Q;License: Standard YouTube License, CC-BY