I am junior teacher of maths in a high school in Netherlands. Right
now I am working on the ?Mathematics in historical perspective:
special numbers (specifically e)? subject. I need a sample lesson
about number e in general or some characteristics of e (for example
irrationality of e or e^x).  I need a lesson that could be given in a
high school, gymnasium or college. Lesson needs to contain some theory
and along with that also information about history and historical
development of the knowledge about e. Could you please provide me such
a lesson?

---

Request for Question Clarification by mathtalk-ga on 10 Jun 2004 16:42 PDT

Hi, tofig_hamidov-ga:

When you say a lesson that could be given in "a high school, gymnasium
or college", I'm a bit uncertain as to whether you mean a lesson could
be given in all of these settings or in at least one of them.

In particular please describe the background of the students for whom
the lesson should be planned.  Will they have studied logarithms,
exponents, and trigonometric functions?  Will they have studied
calculus, or even differential equations?

The simplest lesson about e that I can think of right now would be to
discuss a way of defining e as the limit of (1 + 1/n)^n  as n =
1,2,3,... tends to infinity.  The lesson would involve converge of
sequences.

Naturally if you've had experience in teaching mathematics, you'll
have some thoughts of your own about preparing such a lesson plan. 
Given that you've found the efforts of one Researcher insufficient
already, the more clarity you can provide about what would acceptable
as an Answer, the more easily another Researcher will be able to judge
if it can be done well for the current List Price offered.

regards, mathtalk-ga

I saw some good infor here:
www-gap.dcs.st-and.ac.uk/~history/HistTopics/e.html

Perhaps you could get one hundred or so students to form a "human
slide rule" using colored and numbered cards.

Good luck,
         Ed V.

I recommend you pick up a copy of "e: The Story of a Number", by Eli
Maor (http://www.amazon.com/exec/obidos/tg/detail/-/0691058547/qid=1086906213/sr=8-3/ref=pd_ka_3/103-2577821-4427859?v=glance&s=books&n=507846).
 You can probably check out a copy at a local library.  It won't
provide you with a lesson plan, per se, but would certainly give you
exactly the background information you would need to put such a plan
together.

I need actual lesson, not information about E. Please send me a
concrete lesson, which I could use.  I already used a lot of
information for this project from ?Ask Dr. Math?
(http://mathforum.org/dr.math/) and many others describing e and
telling about history of e, but none of them is a concrete sample
lesson. And definitely I did not ask for advising me a book "e: The
Story of a Number". I already have it and used?

Please give a better answer or remove your comments.

Regards,

Tofig

I regret that I did not post a comment before hedgie posted an answer,
emphasizing your response to my previous answer: that you specifically
needed a lesson about e, not material that you might adapt into a
lesson.

justaskscott wrote:

" I regret that I did not post a comment before hedgie posted an answer .."

 Indeed, it could save me a bit of work. 

 However, considering the fact I have found two quite concrete and
tested    Lesson Plans,  I would probably post my answer anyway.
 
 I would just leave out some additional background material which was
included to allow teacher to customise and enrich the plans which were
referenced in my answer.


hedgie.