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The power of exponentiation, equation #3 has a typo.
(n^m)^p is incorrectly shown as n^(np) instead of n^(mp)
Oops (for at least the fourth time) – will fix, thanks
Fixed and acknowledged at: https://peterjamesthomas.com/maths-science/eulers-number/#acknowledgements Please tell me if there is a site that you would like me to link your name to. Thanks again Peter
In your explanation of Euler’s Number in the section on What Difference Does It Make the graph to show the slipe at point x shows instead the average slope from x to a random point above x defined by the red triangle. Wouldn’t the point x slope actually be the tangent to point x and why wouldn’t that be explained more clearly? Everything else was amazing in the space provided!
The limit of the slope of the triangle,as the length of its base tends to zero, would be the slope at x. This is identical to the slope of the tangent line at x.
Thank you for the reply. I still wonder why you wouldn’t just use the tangent on its own? Is that to illustrate the use of limits in the evolutuin of the mathematics?
So you are familiar with the concept of tangent to a curve. Not everyone who reads this article will be. I have already introduced a lot of terms and concepts and there is no need to add one more if I can tell my story perfectly adequately without. I understand where you are coming from and would encourage you to write your own article explaining tangents to curves. I agree that would be a useful thing to read. My article was already over 6,000 words. Peter
Thanks Peter! I couldn’t begin to write that paper!
I struggled with calculus but learned about inflection points on curves in high school and reviewed them with an economics professor in college. You’re article was great. It woke up a part of my brain I hadn’t entertained for a while!
Happy to hear about your reawakening – Peter
Very much enjoying your new book, Glimpses of Symmetry!
A couple of corrections & suggestions (so far)…
Chapter 2, What is a Group:
Suggestion: Consider Introducing the term “Abelian group” in the text of chapter 2, where you first define Commutative group, rather than in a separate footnote [13]. Not everyone reads the footnotes immediately, and may be confused seeing the term referenced later in the chapter.
Chapter 3, Shifting Shapes:
“A turn through 120° clockwise leaves the triangle in place, but the red vertex is now on the left, the blue one is at the top and the green one is to the left.”
Should be:
“A turn through 120° clockwise leaves the triangle in place, but the red vertex is now on the right, the blue one is at the top and the green one is to the left.”
Thanks.
Hello,
Thanks for the positive feedback and the suggestions (both Chapter 3 I think). I should have fixed both now thank you :-).
Very happy to receive feedback and will add you to the acknowledgements when I get time. Any particular web-site I should link back to?
All the best
Peter