Type:

Interactive

Description:

<p>This exploration leads calculus students, discussing the work in trios or quartets, to formulate Euler's Identity: e^(ipi)+1=0, a beautiful equation holding 5 important numbers (0,1,e,pi,i the imaginary root of -1) and the basic operations of adding, multiplying, and exponentiation. &nbsp;When can you give this to students? &nbsp;After they know the basic trig derivatives &amp; quotient rule. &nbsp;There are other lessons where you prove the same formula with infinite series for sin x &amp; cos x, but this introduces the equation earlier in the course of calculus, to inspire students to study some of beautiful topics in Calculus C and Complex Analysis in college. &nbsp;Hat tip to Dr. Roberto Martinez for showing me this proof, which I put in worksheet form.</p>

Subjects:

  • Mathematics > General
  • Mathematics > Calculus
  • Mathematics > Trigonometry

Education Levels:

  • Grade 11
  • Grade 12
  • Higher Education
  • Graduate
  • Undergraduate-Upper Division
  • Undergraduate-Lower Division

Keywords:

e^(ipi)+1 trig identities quotient rule pi imaginary root of -1 complex numbers complex analysis

Language:

English

Access Privileges:

Public - Available to anyone

License Deed:

Public Domain

Collections:

None
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Curriki Rating
On a scale of 0 to 3
3
On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2003-12-14.

Component Ratings:

Technical Completeness: 3
Content Accuracy: 3
Appropriate Pedagogy: 3

Not Rated Yet.

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