**ETGAR-GILYONOT MATEMATIKA**
was a periodical for mathematically oriented high-school students
published by the Mathematics Departments of
the Weizmann Institute and/or the Technion and/or the University of Haifa.

Among its editors were J. Gillis Z"L (Weizmann), Avi Berman, Zvi Har'El Z"L, Eliahu Levy and Ron Holzman (Technion), and in the last years Shay Gueron (Haifa Univ.).

Our hope is to post here articles that appeared in ETGAR-GILYONOT MATEMATIKA (and maybe new articles too, contributed by the interested community).

**Etgar Hadash - Net-Gar
אתגר חדש
- נטגר
- an online new Etgar.**

(A booklet of articles which I wrote there:
pdf.
Re the article there about pi: see also
Jonathan M. Borwein and Scott T. Chapman's talk
for pi's day, with references to more proofs for (Euler's) famous formula
for the sum of the series of the reciprocals of the squares of the natural numbers.)

There,
or here,
one can find old ETGAR-GILYONOT MATEMATIKA issues scanned by the
Israel Mathematical Union.

**E.L.** A remark about proving the irrationality of square roots (re Michael Cwikel's article in
נטגר No. 8, October 2014)
pdf.

**Articles by Paul Erdös
**

**ETGAR-GILYONOT MATEMATIKA** and its predecessor **GILYONOT MATEMATIKA**
had the great privilege of including a few articles contributed by Paul Erdös.

**Paul Erdös**: Some Problems (Solved and Unsolved) in Number Theory and Geometry
ps
pdf

**Paul Erdös**: On Some Problems in Elementary Geometry (Hebrew)
ps
pdf

**Some new articles **

**Eliahu Levy**:
The Millennium Prize Problems (Hebrew)
ps
pdf
(see also in Net-Gar נטגר),
Circle Tangent to Circles and Triangle (A Japanese Sangaku Problem) (Hebrew)
ps
pdf
(see also in Net-Gar נטגר),
The Impossibility of Trisecting an Angle by Ruler and Compass and a Sad Story (Hebrew)
pdf
(see also in Net-Gar נטגר),
Some Fun with Inversion in 3-Space (Hebrew)
ps
pdf,
Hilbert's Proof for Lindemann's Theorem about e and π (Hebrew)
ps
pdf,
Some Fun with Integrals (Hebrew)
ps
pdf

**Tomer Peleg**:
Proof and Construction for Circle Tangent to Circles and Triangle (A Japanese Sangaku Problem) (Hebrew)
pdf,
Further Questions and Suggestions, Archimedes' Twins (Hebrew)
pdf,
Here: about Sangaku, Archimedes' twins.

(E.L.: another proof, using inversion (Hebrew) pdf, a proof for Archimedes' twins, using parabolas (Hebrew) pdf)

**Simeon Reich (now professor at the Technion) - articles from GILYONOT MATEMATIKA, the 1960's:**
Fibonacci Numbers (Hebrew)
pdf,
On an Algebra Problem (Hebrew)
pdf,
On a Certain Functional Equation (Hebrew)
pdf,
A Short Proof: If Two Bisectors in a Triangle are Equal, the Triangle is Isosceles (Hebrew)
pdf

**E.L.** D-tables and the representation of quadratic irrationals as continued fractions
(Hebrew, an old text of mine)
word file.

**E.L.: Did you know ? - vignettes from the history of mathematics (Hebrew):**

The Ancient Babylonians' Place-Value System of 60,

The Ancient Greek Mathematics,

The Algorists and the Abacists,

Negative Numbers,

The Invention of Print and the Invention of the Computer.

**Some oldies but goldies from ETGAR-GILYONOT MATEMATIKA
**

**Prof. Ron Aharoni (Technion)**:
Majorization (Hebrew)
ps
pdf,
The Paradoxes (Hebrew)
ps
pdf,
Probabilistic Paradoxes (Hebrew)
ps
pdf

**Dr. E. Altman Z"L**: Calculating the Volume of Special Tetrahedrons (Hebrew)
ps
pdf

**Tsachik Gelander (now professor at the Hebrew Univ.)**:
Inversion (in circles) (Hebrew)
pdf,
Several Proofs for a Well-Known Geometry Problem (Hebrew)
ps
pdf,
The Microbe and the Drunkard (Hebrew)
ps
pdf

**Prof. J. Gillis Z"L**:
Euler's Transform (Hebrew)
ps
pdf

Two articles after lectures given at the Technion by
**Prof. Daniel J. Kleitman** and **Prof. Gil Kalai**:

Cayley's Formula (Hebrew)
ps
pdf,
Galvin's Proof for Dinitz' Conjecture (Hebrew)
ps
pdf

**Mikhael Kreizman Z"L**:
A Method for Solving Equations with Parameters (Hebrew)
ps
pdf

**Prof. Micha Sharir (Tel-Aviv Univ.)**:
Davenport-Schinzel Sequences (Hebrew)
ps
pdf

A booklet (in Hebrew) with **Eliahu Levy**'s articles in ETGAR-GILYONOT MATEMATIKA (with some addenda)
ps
pdf

(A 2015 remark by
Daniel Reem:
the phenomenon described in my (1996) article on p. 21 -
the probability for a physical constant to begin with the digit 1 -
is called Benford's law, see
here.)

Wonders of the Number Two - an Arabic version, by **Jaudat Rashed Z"L**, of one of the articles in the above booklet (Arabic).

The 1927 Earthquake and its Impact on the Reine Village, by **Jaudat Rashed Z"L** (Hebrew).