This is a “math
story” about the inhabitants of Straight Line and their interesting life. It can
be read by young people of different age, and can teach them different things.
It introduces little children easily and naturally to many fundamental and
sophisticated notions and concepts of geometry and algebra, such as: point (no
measure, as small as one can imagine), line, straight line, ray, segment,
interval, intercept, direction on a line, velocity, relation between distance,
velocity, and time, positive and negative numbers, and numbers’ location on the
Several of my little
friends (6-9 years old) have by now read the story.
followed reflected their attraction and enthusiasm to read and learn more. These
questions invited a teacher/parent/grandparent to develop a topic (or topics)
and explore together with students even more complex areas of mathematics;
predisposition of the audience was already there, which guaranteed or at least
gave a great chance of success.
In a provoking and
intriguing manner, the same story teaches high school children more advanced
mathematics concepts, terminology, phraseology, and notations (for example: a
point A, segment [A, B], interval (AB), complement to a set, real straight line,
infinite line, “at any point on the line”, more on positive and negative numbers,
positive and negative directions on a line, neighborhood of a point, "approaching
a point," symmetry with respect to a point, etc.) A reader begins to understand
that an infinite set on the line is not the same as an enormously long one – a
common misconception many high school students still have.
Meanwhile, the story
gives helpful ideas and hints on important notions and concepts of point-set
topology to college students. Examples: density of points on the line,
complement of a set, closed and open sets, infinite sets.
A game, “Find the closest friend”, in the story gives a clue how to solve
various problems presenting a challenge to some students in my Real Analysis (usually
one for graduating seniors) course.