Problem-Solving Strategies: Research Findings from Mathematics
... more accessible related problem by replacing 1989 by 28, 117 by 4, and 17 by 7, we should try to build up our solution to the problem on {1, 2, ... , 35} upon some modification to the solution of the previous one while keeping as much of the pattern as possible. H we are through with 35, then the ca ...
... more accessible related problem by replacing 1989 by 28, 117 by 4, and 17 by 7, we should try to build up our solution to the problem on {1, 2, ... , 35} upon some modification to the solution of the previous one while keeping as much of the pattern as possible. H we are through with 35, then the ca ...
Chapter 1. Arithmetics
... If two numbers have factors (or divisors) in common, then the largest of these common factors is called their highest common factor (HCF). For example: 18 has the factors 1, 2, 3, 6, 9 and 18; 30 has the factors 1, 2, 3, 5, 6, 15, 30. Consequently, the numbers 1, 2, 3 and 6 are their common factors, ...
... If two numbers have factors (or divisors) in common, then the largest of these common factors is called their highest common factor (HCF). For example: 18 has the factors 1, 2, 3, 6, 9 and 18; 30 has the factors 1, 2, 3, 5, 6, 15, 30. Consequently, the numbers 1, 2, 3 and 6 are their common factors, ...
Full text
... The "angle" we have in mind is a gnomon, a planar region that has the general shape of a carpenterfs square. At the time of Pythagoras, a carpenterfs square was in fact called a gnomon. The term came from Babylonia, where it originally referred to the vertically placed bar that cast the shadow on a ...
... The "angle" we have in mind is a gnomon, a planar region that has the general shape of a carpenterfs square. At the time of Pythagoras, a carpenterfs square was in fact called a gnomon. The term came from Babylonia, where it originally referred to the vertically placed bar that cast the shadow on a ...
Full text
... As an example, let an ~ 2ft ifftis prime and 2ft + 1 otherwise. Then fe = I = 1 in Theorem 2, and {an} is a (3, 2)-arithmetic sequence. Actually, {an} is also a (2, 2)-arithmetic sequence, which is saying more. This example shows that the fe and I in Theorem 2 need not be the least values for which ...
... As an example, let an ~ 2ft ifftis prime and 2ft + 1 otherwise. Then fe = I = 1 in Theorem 2, and {an} is a (3, 2)-arithmetic sequence. Actually, {an} is also a (2, 2)-arithmetic sequence, which is saying more. This example shows that the fe and I in Theorem 2 need not be the least values for which ...
number systems
... Let us take a look at the number line again. Have you picked up all the numbers? Not, yet. The fact is that there are infinitely many more numbers left on the number line! There are gaps in between the places of the numbers you picked up, and not just one or two but infinitely many. The amazing thin ...
... Let us take a look at the number line again. Have you picked up all the numbers? Not, yet. The fact is that there are infinitely many more numbers left on the number line! There are gaps in between the places of the numbers you picked up, and not just one or two but infinitely many. The amazing thin ...
Bijective Correspondences and Countably Infinite Sets
... Two sets have the same cardinality if �and only if) it is possible to match each element of A to an element of B in such a way that every element of each set has exactly one “partner” in the other set. This might not be particularly important/interesting in the case of finite sets, since we can often ...
... Two sets have the same cardinality if �and only if) it is possible to match each element of A to an element of B in such a way that every element of each set has exactly one “partner” in the other set. This might not be particularly important/interesting in the case of finite sets, since we can often ...
Frequency of Primes Instructions (Word Format)
... twin primes. It is not known whether or not there are an infinite number of such primes. Find the numbers of twin primes in intervals of 100 (1 to 100, 100 to 200, etc.). Form a conjecture about the occurrence of twin primes for such intervals. 3. In #2 you found consecutive primes whose difference ...
... twin primes. It is not known whether or not there are an infinite number of such primes. Find the numbers of twin primes in intervals of 100 (1 to 100, 100 to 200, etc.). Form a conjecture about the occurrence of twin primes for such intervals. 3. In #2 you found consecutive primes whose difference ...