Alexander Soifer | University of Colorado at Colorado Springs (original) (raw)
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Papers by Alexander Soifer
The problem title comes from a famous proverb "To have a cake and eat it too," which in my early ... more The problem title comes from a famous proverb "To have a cake and eat it too," which in my early American years I could not understand. Surely you have to "have a cake" in order "to eat it"! A better formulation of this folk wisdom would have been "To keep a cake and eat it too," which is obviously impossible, hence a moral of the
It is impossible to translate into a written word the excitement of the 30-Year Anniversary Award... more It is impossible to translate into a written word the excitement of the 30-Year Anniversary Award Presentation and the Round Table Panel that took place. Yet, let me attempt to give you a glimpse of this event.
Springer eBooks, 2011
... The Olympiad season commenced on April 19, 2001, with Raquel Rutledge's article “Let the ... more ... The Olympiad season commenced on April 19, 2001, with Raquel Rutledge's article “Let the math games begin” in the Gazette: Solving one of Alexander Soifer's math problems is like finding a treasure. ... 273 Golden middle schooler Bryce Herdt ...
This chapter conveys Van der Waerden work at Hamburg University during 1926–1927 time period.
Springer eBooks, 2011
The First Olympiad was such a success, it received such wonderful media coverage, that I was call... more The First Olympiad was such a success, it received such wonderful media coverage, that I was called into the office of my dean. He went straight to the point: “You ran the Olympiad, I solicited the prizes. What do we need the College of Education for?” “You want to join Education as a co-organizer?” I asked. “No, Engineering alone will run the Olympiad from now on.” “I cannot go to Dennis (Dean of Education), the only person who supported the Olympiad from the start, and tell him to get out.” “I’ll do it myself,” said my dean.
Springer eBooks, 2009
During the years 2002–2004 I was visiting Princeton University with its fabulous mathematics depa... more During the years 2002–2004 I was visiting Princeton University with its fabulous mathematics department, a great fixture of which was a daily coffee hour in the commons room, attended by everyone, from students to the Beautiful Mind (John F.Nash, Jr.). For one such coffee hour I came thinking again about the drawing depicted in this book in Figure 2.2. This time I imagined that we dealt with equilateral triangles, and the crux of the figure was a demonstration that n 2 unit triangles can cover a triangle of side n.
Communications in Algebra, 1987
Springer eBooks, 2010
Imagine you have an m × n rectangle R and lots of dominoes (a domino is a 1 × 2 rectangle). It is... more Imagine you have an m × n rectangle R and lots of dominoes (a domino is a 1 × 2 rectangle). It is easy to find the conditions under which R can be tiled by dominoes, i.e., covered by dominoes, without any dominoes overlapping or sticking out over the boundary of R. Indeed, R can be tiled by dominoes if and only if mn is even (prove it!).
Springer eBooks, 2009
Let us try to solve Grand Problem I. You may recall (Figure 2.2) that every triangle can be cut i... more Let us try to solve Grand Problem I. You may recall (Figure 2.2) that every triangle can be cut into n triangles congruent to each other if n is a perfect square (i.e., n = 1, 4, 9, 25, …). The “only” question that remains is whether a partition into n congruent triangles exists only for perfect squares n.
Springer eBooks, 2011
ABSTRACT Did you enjoyed the Olympiad Problem 19.4? Then brace yourself for much more fun! While ... more ABSTRACT Did you enjoyed the Olympiad Problem 19.4? Then brace yourself for much more fun! While all explorations in different ways are dear to my heart, this small collection may provide the greatest enjoyment of all. Some of these problems have been solved, others are still await- ing their conqueror, but all of them satisfy the definition of “classic” problems of mathematics.
Springer eBooks, 2011
In the Colorado Mathematical Olympiad the same problems are offered to every participant from a s... more In the Colorado Mathematical Olympiad the same problems are offered to every participant from a seventh grader to a senior. This is why they must require minimal bits of knowledge for their solutions, such as the sum of angles in a triangle is equal to 180°, or the three bisectors of a triangle have a point in common. These problems do require a great deal of common sense, creativity, and imagination. Some of the problems model mathematical research: they would capitulate only to experimenting with particular cases, followed by noticing a pattern, followed in turn by generalization, formulation of a hypothesis, and finally by a proof.
Springer eBooks, 2011
The nineteenth Colorado Mathematical Olympiad (CMO-2002) took place on April 19, 2002, the day be... more The nineteenth Colorado Mathematical Olympiad (CMO-2002) took place on April 19, 2002, the day before the third anniversary of the Columbine tragedy. It brought together 614 middle and high school students (a 28% increase from the previous year). Contestants came from all over Colorado: Agate, Aurora, Benett, Black Forest, Brighton, Canon City, Cascade, Centennial, Colorado Springs, Deer Trail, Denver, Dinosaur,
Springer eBooks, 2009
of the IBM Research 2. Hermann W d , Philosophy of Mathematics and Natural Center played a leadin... more of the IBM Research 2. Hermann W d , Philosophy of Mathematics and Natural Center played a leading part in promoting these Science, Princeton, 1949, p. 237. 3. John Riordan, An Introduction to Combinatorial Analysis, activities. In particular, it was Paul Roth who (with Wilev. 1958. the undersigned) initiated the chain of events that 4. Marshall Hall, Jr., "A Survey of Combinatorial Analysis", culminates in this special issue of the IBM Journal.
The problem title comes from a famous proverb "To have a cake and eat it too," which in my early ... more The problem title comes from a famous proverb "To have a cake and eat it too," which in my early American years I could not understand. Surely you have to "have a cake" in order "to eat it"! A better formulation of this folk wisdom would have been "To keep a cake and eat it too," which is obviously impossible, hence a moral of the
It is impossible to translate into a written word the excitement of the 30-Year Anniversary Award... more It is impossible to translate into a written word the excitement of the 30-Year Anniversary Award Presentation and the Round Table Panel that took place. Yet, let me attempt to give you a glimpse of this event.
Springer eBooks, 2011
... The Olympiad season commenced on April 19, 2001, with Raquel Rutledge's article “Let the ... more ... The Olympiad season commenced on April 19, 2001, with Raquel Rutledge's article “Let the math games begin” in the Gazette: Solving one of Alexander Soifer's math problems is like finding a treasure. ... 273 Golden middle schooler Bryce Herdt ...
This chapter conveys Van der Waerden work at Hamburg University during 1926–1927 time period.
Springer eBooks, 2011
The First Olympiad was such a success, it received such wonderful media coverage, that I was call... more The First Olympiad was such a success, it received such wonderful media coverage, that I was called into the office of my dean. He went straight to the point: “You ran the Olympiad, I solicited the prizes. What do we need the College of Education for?” “You want to join Education as a co-organizer?” I asked. “No, Engineering alone will run the Olympiad from now on.” “I cannot go to Dennis (Dean of Education), the only person who supported the Olympiad from the start, and tell him to get out.” “I’ll do it myself,” said my dean.
Springer eBooks, 2009
During the years 2002–2004 I was visiting Princeton University with its fabulous mathematics depa... more During the years 2002–2004 I was visiting Princeton University with its fabulous mathematics department, a great fixture of which was a daily coffee hour in the commons room, attended by everyone, from students to the Beautiful Mind (John F.Nash, Jr.). For one such coffee hour I came thinking again about the drawing depicted in this book in Figure 2.2. This time I imagined that we dealt with equilateral triangles, and the crux of the figure was a demonstration that n 2 unit triangles can cover a triangle of side n.
Communications in Algebra, 1987
Springer eBooks, 2010
Imagine you have an m × n rectangle R and lots of dominoes (a domino is a 1 × 2 rectangle). It is... more Imagine you have an m × n rectangle R and lots of dominoes (a domino is a 1 × 2 rectangle). It is easy to find the conditions under which R can be tiled by dominoes, i.e., covered by dominoes, without any dominoes overlapping or sticking out over the boundary of R. Indeed, R can be tiled by dominoes if and only if mn is even (prove it!).
Springer eBooks, 2009
Let us try to solve Grand Problem I. You may recall (Figure 2.2) that every triangle can be cut i... more Let us try to solve Grand Problem I. You may recall (Figure 2.2) that every triangle can be cut into n triangles congruent to each other if n is a perfect square (i.e., n = 1, 4, 9, 25, …). The “only” question that remains is whether a partition into n congruent triangles exists only for perfect squares n.
Springer eBooks, 2011
ABSTRACT Did you enjoyed the Olympiad Problem 19.4? Then brace yourself for much more fun! While ... more ABSTRACT Did you enjoyed the Olympiad Problem 19.4? Then brace yourself for much more fun! While all explorations in different ways are dear to my heart, this small collection may provide the greatest enjoyment of all. Some of these problems have been solved, others are still await- ing their conqueror, but all of them satisfy the definition of “classic” problems of mathematics.
Springer eBooks, 2011
In the Colorado Mathematical Olympiad the same problems are offered to every participant from a s... more In the Colorado Mathematical Olympiad the same problems are offered to every participant from a seventh grader to a senior. This is why they must require minimal bits of knowledge for their solutions, such as the sum of angles in a triangle is equal to 180°, or the three bisectors of a triangle have a point in common. These problems do require a great deal of common sense, creativity, and imagination. Some of the problems model mathematical research: they would capitulate only to experimenting with particular cases, followed by noticing a pattern, followed in turn by generalization, formulation of a hypothesis, and finally by a proof.
Springer eBooks, 2011
The nineteenth Colorado Mathematical Olympiad (CMO-2002) took place on April 19, 2002, the day be... more The nineteenth Colorado Mathematical Olympiad (CMO-2002) took place on April 19, 2002, the day before the third anniversary of the Columbine tragedy. It brought together 614 middle and high school students (a 28% increase from the previous year). Contestants came from all over Colorado: Agate, Aurora, Benett, Black Forest, Brighton, Canon City, Cascade, Centennial, Colorado Springs, Deer Trail, Denver, Dinosaur,
Springer eBooks, 2009
of the IBM Research 2. Hermann W d , Philosophy of Mathematics and Natural Center played a leadin... more of the IBM Research 2. Hermann W d , Philosophy of Mathematics and Natural Center played a leading part in promoting these Science, Princeton, 1949, p. 237. 3. John Riordan, An Introduction to Combinatorial Analysis, activities. In particular, it was Paul Roth who (with Wilev. 1958. the undersigned) initiated the chain of events that 4. Marshall Hall, Jr., "A Survey of Combinatorial Analysis", culminates in this special issue of the IBM Journal.