**Abstracts of the papers in “Journal of Recreational Mathematics” Volume 1, Number 1, 1968**

Given the elapsed time since these papers
appeared and that there were no abstracts with the originals, all of the items
in this list were written by Charles Ashbacher.

“Magic Designs,” by Robert B. Ely,
III

**Abstract**

The definition of a magic design is as
follows:

A design with N parts is said to be
magic, if those parts can be labeled with the numbers 1 to N so that the labels
of each of a number of identical sub-designs give the same constant total.

A magic square, which is an m x m grid where
each row and column has the same sum is
the most widely known magic design.

In this paper, additional magic designs, such
as a triangle, cube, a grid made of hexagons, a triangular grid and the faces
of a dodecahedron are analyzed.

“Counting Planar Maps,” by W. T.
Tutte

**Abstract**

The paper opens with the examination of a
standard die as an object having six faces. Such an object is called a
hexahedra. There are seven convex objects having exactly six faces and three
that are concave. Schlegel diagrams are used to convert the polyhedra into
planar graphs for further analysis. Planar diagrams that can be defined by
3-connected graphs are called c-nets.

A table of the number of c-nets for
each number of edges for n from 4 through 25 is given along with the explicit
formula used to compute the numbers.

“Infinite Geometry,” by Donald L.
Vanderpool

**Abstract**

While Euclidean geometry is performed on a
plane infinite in two directions, triangles are described as being finite. In
this paper, the lines that form the triangles are geodesic’s in Einstein’s
4-dimensional space. This leads to three-sided figures where the sums of the
angles are vastly different from the standard 180 degrees.

“A Recurrent Operation Leading to a
Number Trick,” by Charles W. Trigg

**Abstract**

For each two-digit number S, the digits are
written in reverse order. This is added to the sum of the digits of S and then
the sum is reduced modulo 100. The computations are then repeated.

Under this operation, the fifty-two odd
two-digit numbers form a series in which the last 6 numbers form a closed loop.

“Alphametics,” by J. A. H. Hunter

**Abstract**

This paper re-introduces the letter-arithmetic
puzzle of alphametic and gives a brief description of the logic one uses to
solve them. The example problem is a division alphametic.

“The Witch of Agnesi,” by Harold D.
Larsen

**Abstract**

The Witch of Agnesi is a curve defined by the
equations:

y( a

^{2}+ x^{2}) = a^{3}or x = a(cot θ), y = a(sin θ)^{2}.
The history and some of the major properties
of this curve are examined.

“Curiosa for 1968,” by Charles W.
Trigg

**Abstract**

This paper gives several ways that 1968 can be
written using conventional math symbols and the nine decimal digits.

“Pentomino Farms,” by Fr. Victor
Feser, OSB

**Abstract**

The 12 pentominoes are formed from five
squares being connected edge-to-edge. A pentomino farm is a rectangular shape
made by the set of pentominoes that has enclosed open space(s). Several of the
most basic are presented.

“Squares with 9 and 10 Distinct
Digits,” by T. Charles Jones

**Abstract**

In this paper, two computer generated tables
are given. The first contains all squares with nine distinct digits and the
second all squares with ten distinct digits.

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