This is about an image that is intended

- to be decorative,
- to establish the mathematical construction, with ruler and compass, of points of an ellipse.

Ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ πλάγχθη

February 3, 2023 – 2:08 pm

This is about an image that is intended

- to be decorative,
- to establish the mathematical construction, with ruler and compass, of points of an ellipse.

September 21, 2020 – 7:08 pm

I say that mathematics is the deductive science; and yet there would seem to be mathematicians who disagree. I take up two cases here.

August 5, 2020 – 6:26 pm

This past spring (of 2020), when my university in Istanbul was closed (like all others in Turkey) against the spread of the novel coronavirus, I created for my students an exercise, to serve at least as a distraction for those who could find distraction in learning.

*Note added, April 17, 2023:* An account of the mathematics involved in the exercise would ultimately be published as: Pierce, D. (2021). “Conics in Place.” *Annales Universitatis Paedagogicae Cracoviensis* | *Studia Ad Didacticam Mathematicae Pertinentia,* **13,** 127–150.

February 24, 2020 – 7:06 am

Because Herman Wouk was going to put physicists in a novel, Richard Feynman advised him to learn calculus: “It’s the language God talks.” I think I know what Feynman meant. Calculus is the means by which we express the laws of the physical universe. This is the universe that, according to the mythology, God brought into existence with such commands as, “Let there be light.” Calculus has allowed us to refine those words of creation from the Biblical account. Credited as a discover of calculus, as well as of physical laws, Isaac Newton was given an epitaph (ultimately not used) by Alexander Pope:

Nature and Nature’s laws lay hid in night:God said, Let Newton be! and all was light.

I don’t know, but maybe Steven Strogatz quotes Pope’s words in his 2019 book, *Infinite Powers: How Calculus Reveals the Secrets of the Universe.* This is where I found out about Wouk’s visit with Feynman. I saw the book recently (Saturday, February 22, 2020) in Pandora Kitabevi here in Istanbul. I looked in the book for a certain topic that was of interest to me, but did not find it; then I found a serious misunderstanding.

April 17, 2019 – 2:21 pm

After Descartes gave geometry the power of algebra in 1637, a purely geometrical theorem of Apollonius that is both useful and beautiful was forgotten. This is what I conclude from looking at texts from the seventeenth century on.

October 10, 2014 – 3:50 pm

Here is the model that I made of the hyperbola, or rather the **conjugate hyperbolae,** as Apollonius calls them.

Continue reading

October 8, 2014 – 11:19 am

I do not now recall my specific inspiration; but in January of 2012, sitting at home in Istanbul, I cut up a cardboard box in order to make a model of a parabola *quâ* conic section.

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January 25, 2014 – 7:17 am

In Chapter I of *The New Leviathan,* we stipulated that natural science, the “science of body,” must be free to pursue its own aims. But we ourselves are doing science of mind, and:

1. 85.The sciences of mind, unless they preach error or confuse the issue by dishonest or involuntary obscurity, can tell us nothing but what each can verify for himself by reflecting on his own mind.

All of us can be scientists of mind, if only we are capable of reflection: Continue reading

May 14, 2013 – 11:23 am

This is mostly reminiscences about high school. I also give some opinions about how mathematics *ought* to be learned. The post originally formed one piece with my last article, “Limits.”

I learned calculus, and the epsilon-delta definition of limit, in Washington D.C., in my last two years at St Albans School, in a course taught by a peculiar fellow named Donald J. Brown. The first of these two years was officially called Precalculus Honors, but some time in that year, we started in on calculus proper.

May 4, 2013 – 12:54 pm

This is about limits in mathematics: both the technical notion that arises in calculus, and the barriers to comprehension that one might reach in one’s own studies. I am going to say a few technical things about the technical notion, but there is no reason why this should be a barrier to your reading: you can just skip the paragraphs that have special symbols in them.

Looking up something else in the online magazine called *Slate,* I noted a reprint of an article called “What It Feels Like to Be Bad at Math” from a blog called *Math With Bad Drawings* by Ben Orlin. Now teaching high-school mathematics, Mr Orlin recalls his difficulties in an undergraduate topology course. His memories help him understand the difficulties of his own students. When students do not study, why is this? It is because studying makes them conscious of how much they do not understand. They feel stupid, and they do not like this feeling. Continue reading