Portal through Mathematics is a collection of
puzzles and problems mostly on topics relating to secondary
mathematics. The problems and topics are fresh and interesting and
frequently surprising. One example: the puzzle that asks how much
length must be added to a belt around the Earth's equator to raise it
one foot has probably achieved old chestnut status. Ivanov, after
explaining the surprising answer to this question, goes a step further
and asks, if you grabbed that too long belt at some point and raised
it as high as possible, how high would that be? The answer to that is
more surprising than the classic puzzle's answer. The book is
organized into 29 themes, each a topic from algebra, geometry or
calculus and each launched from an opening puzzle or problem. There
are excursions into number theory, solid geometry, physics and
combinatorics. Always there is an emphasis on surprise and
delight. And every theme begins at a level approachable with minimal
background requirements. With well over 250 puzzles and problems,
there is something here sure to appeal to everyone.
Portal through Mathematics will be useful for prospective
secondary teachers of mathematics and may be used (as a supplementary
resource) in university courses in algebra, geometry, calculus, and
discrete mathematics. It can also be used for professional development
for teachers looking for inspiration. However, the intended audience
is much broader. Every fan of mathematics will find enjoyment in
it.