· Every angle can be trisected using a compass and marked straightedge. The following construction is due to Archimedes. Assume the compass has two marks on it, a distance r apart. Let ZBAC be an angle. Draw a circle y of radius r and center A. The circle will intersect both sides of the angle; in order to simplify the notation let us assume that B and C lie on the circle. Place the straightedge so that it passes through C and so that one mark is at a point D on y and the other is at a point E on "AB. (See Figure 9.17.) Use the Isosceles Triangle Theorem and the Euclidean Angle Sum Theorem to prove that u(2CEB) = (1/3)µ(LCAB). D E A
· Every angle can be trisected using a compass and marked straightedge. The following construction is due to Archimedes. Assume the compass has two marks on it, a distance r apart. Let ZBAC be an angle. Draw a circle y of radius r and center A. The circle will intersect both sides of the angle; in order to simplify the notation let us assume that B and C lie on the circle. Place the straightedge so that it passes through C and so that one mark is at a point D on y and the other is at a point E on "AB. (See Figure 9.17.) Use the Isosceles Triangle Theorem and the Euclidean Angle Sum Theorem to prove that u(2CEB) = (1/3)µ(LCAB). D E A
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:2. Every angle can be trisected using a compass and marked straightedge. The following
construction is due to Archimedes. Assume the compass has two marks on it, a distance
r apart. Let ZBAC be an angle. Draw a circle y of radius r and center A. The circle will
intersect both sides of the angle; in order to simplify the notation let us assume that B
and C lie on the circle. Place the straightedge so that it passes through C and so that
one mark is at a point D on y and the other is at a point E on `AB. (See Figure 9.17.)
Use the Isosceles Triangle Theorem and the Euclidean Angle Sum Theorem to prove
that u(2CEB) = (1/3)µ(LCAB).
FIGURE 9.17: Archimedes' trisection using a marked straightedge
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
