## It’s All Greek to Me

When my son Sergei made it to the International Linguistics Olympiad I got very excited. After I calmed down I realized that training for this competition is not easy because it is very difficult to find linguistics puzzles in English. This in turn is because these Olympiads started in the USSR many years ago and were adopted here only recently. So I started translating problems from Russian and designing them myself for my son and his team. For this particular problem I had an ulterior motive. I wanted to remind my son and his team of rare words in English with Greek origins. Here is the problem:

We use many words that have Greek origins, for example: amoral, asymmetric, barometer, chronology, demagogue, dermatology, gynecologist, horoscope, mania, mystic, orthodox, philosophy, photography, polygon, psychology, telegram and telephone. In this puzzle, I assume that you know the meanings of these words. Also, since I am a generous person, I will give you definitions from Answers.com of some additional words derived from Greek. If you do not know these words, you should learn them, as I picked words for this list that gave me at least one million Google results.

- Agoraphobia — an abnormal fear of open or public places.
- Anagram — a word or phrase formed by reordering the letters of another word or phrase, such as satin to stain.
- Alexander — defender of men.
- Amphibian — an animal capable of living both on land and in water.
- Anthropology — the scientific study of the origin, the behavior, and the physical, social, and cultural development of humans.
- Antipathy — a strong feeling of aversion or repugnance.
- Antonym — a word having a meaning opposite to that of another word.
- Bibliophile — a lover of books or a collector of books.
- Dyslexia — a learning disability characterized by problems in reading, spelling, writing, speaking or listening.
- Fibromyalgia — muscle pain.
- Hippodrome — an arena for equestrian shows.
- Misogyny — hatred of women.
- Otorhinolaryngology — the medical specialty concerned with diseases of the ear, nose and throat.
- Pedophilia — the act or fantasy on the part of an adult of engaging in sexual activity with a child or children.
- Polygamy — the condition or practice of having more than one spouse at one time.
- Polyglot — a person having a speaking, reading, or writing knowledge of several languages.
- Tachycardia — a rapid heart rate.
- Telepathy — communication through means other than the senses, as by the exercise of an occult power.
- Toxicology — the study of the nature, effects, and detection of poisons and the treatment of poisoning.

In the list below, I picked very rare English words with Greek origins. You can derive the meanings of these words without looking in a dictionary, just by using your knowledge of the Greek words above.

- Barology
- Bibliophobia
- Cardialgia
- Dromomania
- Gynophilia
- Hippophobia
- Logophobia
- Misandry
- Misanthropy
- Misogamy
- Monandry
- Monoglottism
- Mystagogue
- Pedagogue
- Philanthropism

Here are some other words. You do not have enough information in this text to derive their definitions, but you might be able to use your erudition to guess the meaning.

- Antinomy
- Apatheist
- Axiology
- Dactyloscopy
- Enneagon
- Oology
- Paraskevidekatriaphobia
- Philadelphia
- Phytology
- Triskaidekaphobia

## Angelo Scordo:

I am passionate about polyhedra, I recently read the postulate 16 of book 13 of Euclid’s elements and I was particularly impressed so that I had memorized some ancient Greek passages by heart.

I see myself in Alexandria of Egypt instead of Euclid while teaches his disciples a lesson in the fourth century b.c.

I’d like to share some steps with you:

The postulate 16 demonstrates how to inscribe an icosahedron inside a sphere by constructing two regular pentagons inscribed within the relative circles and rotated among them by 36 degrees.

These pentagons then form two pentagonal pyramids that connect the sides of the base to the related vertex.

At the end of this long and accurate demonstration Euclide concludes as follows with the final “Corollary”.

Ἐκ δὴ τούτου φανερόν, ancient greek

By virtue of what I have shown above (ie the demonstration of how an icosahedron is inscribed in the sphere).

ὅτι ἡ τῆς σφαίρας διάμετρος δυνάμει πενταπλασίων ἐστὶ τῆς ἐκ τοῦ κέντρου τοῦ κύκλου, ἀφ’ οὗ τὸ εἰκοσάεδρον ἀναγέγραπται, ancient greek

I can state that the diameter of the sphere at the square is five times the distance from the center of the circle used to build the icosahedron,

(Explanation: Let us think of two opposing vertices one in the upper pentagon and the other in the lower pentagon of the icosahedron. Being opposite vertices their distance is equal to the diameter of the sphere. If we trace a segment that goes from the top vertex up to plane of the pentagon below, this segment as shown by Euclid, is equal to the radius of the circle in which the petagon is inscribed. Then we connect this point to the opposite vertex, this distance is equal to the diameter of the circle in which pentagon is inscribed.

Since the triangle thus formed is rectangular we will have the hypotenuse (diameter of the sphere) squared to be the square of the radius of the circle in which the pentagon is inscribed plus the square of the diameter of the circle ie 4 squares of the radius for a total of 5 squares of the radius. Euclid continues as follows:)

καὶ ὅτι ἡ τῆς σφαίρας διάμετρος σύγκειται ἔκ τε τῆς τοῦ ἑξαγώνου καὶ δύο τῶν τοῦ δεκαγώνου τῶν εἰς τὸν αὐτὸν κύκλον ἐγγραφομένων. ancient greek

I also state that the diameter of the sphere corresponds to one side of a hexagon plus two sides of a decagon, inscribed in the same circle.

(Explanation: think of the two equal pentagonal pyramids and rotated 36 degrees, their bases are separated by a distance equal to the radius of the circle in which the pentagon is inscribed (ie the side of inscribed hexagon), the pyramids instead have for height the side of the decagon. We know today that the side of a decagon is equal to 1 / golden ratio.

Now 2 * (1 / golden section) = sqrt (5) -1, let’s add 1 we get sqrt (5). In his Elements Euclid has never used a formula (the formulas will be introduced more than a thousand years later) but concepts well known to his disciples as the sides of the hexagon and the decagon.

Eventually Euclid says:

ὅπερ ἔδει δεῖξαι

QED (quod erat demonstrandum)

4 January 2019, 4:07 pmwhat I was trying to demonstrate.