Tag Archives: 2026

Seventeen Sides

July 11, 2026 – 6:39 pm

Here are my slides on the construction of the heptakaidecagon. I have referred to them before, as detailed below, but I have edited them (slightly) since, and I wanted to have a fixed home for them. That will be this post.

I call them slides, because the page size is A6, in landscape orientation, and most pages are self-contained, except for the six pages of the Introduction. There are 80 pages, all told, last edited June 13 of this year (2026). A circle is divided into seventeen equal arcs, with ruler and compass alone, and then a proof that the circle has been so divided is given in Euclidean terms.

One purpose then is to contemplate why the Ancients did not discover the construction.

Lying on edge against a backdrop of pine trees and oleander, steel rods trace out the edges of shallow pyramids on square bases, with perpendiculars dropped from the apices to the edges of those bases

Some polygons in three dimensions:
Unused supports for beach umbrellas
Thursday, June 4, 2026
(All photos on this page from Altınova, Ayvalık, Balıkesir, Turkey)

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By David Pierce | Posted in Exposition, Mathematics | Also tagged , , | Comments (0)

An Antithesis

June 1, 2026 – 9:43 am

A text for this post is from Wendell Berry:

Justice is a rational procedure. Mercy is not a procedure and it is not rational. It is a kind of freedom that comes from sympathy, which is to say imagination – the felt knowledge of what it is to be another person or another creature. It is free because it does not have to be just. Justice is desirable, of course, but it is virtually the opposite of mercy. Mercy, says the Epistle of James, “rejoiceth against judgment.”

That is from an essay published originally in Citizenship Papers (2003); I am reading it in Essays 1993–2017 (Library of America, 2019). The quoted essay is called “Two Minds”: those minds are rational and sympathetic respectively. Although Berry does not use the term here, I would say that those two minds are in antithesis.

Seen from a beach, two fully clothed woman stand against the sea, holding up mobiles, one facing the sea obliquely, the other walking along the shore; in the sea, a woman and man stand together, in bikini and trunks respectively. Beyond them all, two breakwaters in line, parallel to the shore, made of rubble

I often read Berry at a beach that is in antithesis to Lesbos. Continue reading →

By David Pierce | Posted in Nature, Pirsig | Also tagged , , , , , , , | Comments (0)

Geometry and Algebra

April 30, 2026 – 5:45 pm

Photo: Appearing the same size are the Eiffel Tower in the distance and a model in the foreground, standing on the railing of a window that overlooks other buildings

From a flat on the rue Saint-Jacques, Paris
Thursday, June 4, 2015

What René Descartes says here does not make a lot of sense to me:

it is far better never to contemplate investigating the truth about any matter than to do so without a method. For it is quite certain that such haphazard studies and obscure reflections blur the natural light and blind our intelligence.

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By David Pierce | Posted in Euclid, Mathematics | Also tagged , | Comments (1)

Ars Longa

April 7, 2026 – 7:44 am

The extant works of Hippocrates take up ten volumes of the Loeb Classical Library. I’ve got the fourth of those volumes, because it contains also the extant fragments of Heraclitus, collected under the title ΠΕΡΙ ΤΟΥ ΠΑΝΤΟΣ, On the Universe. [See the footnote on this title.]

I am going to look here at some aphorisms of Heraclitus, Parmenides, Turkish folklore, Zen, and Erich Segal – also of Hippocrates, who seems to be the source of our word “aphorism.” He wrote ΑΦΟΡΙΣΜΟΙ, and they turn out be in the same Loeb volume with Heraclitus.

Book and paraphernalia lie on one picnic table among several. Two people sit at a table in the distance. The tables are partially shaded by trees, and a bit of sea is visible through other trees

I was reading Parmenides
in Kireçburnu Çamlık Parkı
Erguvantepe, Sarıyer, Istanbul
July 6, 2025

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By David Pierce | Posted in Collingwood, Turkish | Also tagged , , , , , | Comments (1)

Contradiction in Terms

March 31, 2026 – 9:26 pm

Somebody else can amuse us or frighten us. They might put us to sleep with an injection, or perhaps keep us awake. They cannot make us rational. They cannot make us think. Thinking is up to us.

View down a shallow valley of trees and apartment buildings towards water and hills beyond; clear sky above
Our Bosphorus view
from a local mosque, Ecdat Cami
Tarabya, Sarıyer, Istanbul
Monday, February 16, 2026

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By David Pierce | Posted in Collingwood | Also tagged | Comments (1)

Organ Recital

February 14, 2026 – 7:59 am

Trigger warnings for this post:

  1. Suffering and pain.
  2. Cessation of life.
  3. Mathematics.

After the post of December 9, for some reason I wanted to record here a surgical operation in 2019. Then I became preoccupied with mathematics.

Against a concave white wall, a line of rough masks, two eye-holes each, made of tree bark
Hera Büyüktaşcıyan, “Dendrologia,” 2023; part of an exhibit called Phantom Quartet at Arter Istanbul, visited Wednesday, February 4, 2026. The bark of the masks is said to be taken from dead trees on the Isle of Vassivière in the artificial Lac de Vassivière, Limousin, France

On the subject of mathematics, let me take the opportunity to recommend “The Tool/Weapon Duality of Mathematics,” by Alexandre Borovik, recently published in the Journal of Humanistic Mathematics (volume 16, number 1, January 2026; pages 365–392). Continue reading →

By David Pierce | Posted in Istanbul, Plato, Principles of Art, Turkey | Also tagged , , , , , , | Comments (3)