Transcript MATH DAY 2012*Team Competition

An excursion through mathematics and its history
MATH DAY 2012—TEAM
COMPETITION
A quick review of the rules
 History (or trivia) questions alternate with math questions
 Math questions are numbered by MQ1, MQ2, etc. History




questions by HQ1, HQ2, etc.
Math answers should be written on the appropriate sheet
of the math answers booklet.
History questions are multiple choice, answered using the
clicker.
Math questions are worth the number of points shown on
the screen when the runner gets your answer sheet. That
equals the number of minutes left to answer the question.
Have one team member control the clicker, another one
the math answers booklet
Rules--Continued
 All history/trivia questions are worth 1 point.
 The team with the highest math score is
considered first. Next comes the team with
the highest history score, from a school
different from the school of the winning math
team. Finally, the team with the highest
overall score from the remaining schools.
HQ0-Warm Up, no points
 Non Euclidean Geometry is so called because:
A. It was invented by Non Euclid.
B. It negates Euclid’s parallel postulate.
C. It negates all of Euclid’s postulates.
D. Euclid did not care for it.
E. Nobody really knows why it is so called..
HQ0-Warm Up, no points
 Non Euclidean Geometry is so called because:
A. It was invented by Non Euclid.
B. It negates Euclid’s parallel postulate.
C. It negates all of Euclid’s postulates.
D. Euclid did not care for it.
E. Nobody really knows why it is so called..
20 seconds
HQ0-Warm Up, no points
 Non Euclidean Geometry is so called because:
A. It was invented by Non Euclid.
B. It negates Euclid’s parallel postulate.
C. It negates all of Euclid’s postulates.
D. Euclid did not care for it.
E. Nobody really knows why it is so called..
Time's Up!
HQ0-Warm Up, no points
 Non Euclidean Geometry is so called because:
A. It was invented by Non Euclid.
B. It negates Euclid’s parallel postulate.
C. It negates all of Euclid’s postulates.
D. Euclid did not care for it.
E. Nobody really knows why it is so called..
Time's Up!
Demonstrating the points
system
 For math questions there will be a number in
the lower right corner. It will change every
minute. Here I am illustrating with numbers
changing every 10 seconds. Try to imagine 10
seconds is a minute. The first number tells
you the maximum number of points you can
get for the question. Assume a question is on
the screen.
Demonstrating the point
system
 For math questions there will be a number in
the lower right corner. It will change every
minute. Here I am illustrating with numbers
changing every 10 seconds. Try to imagine 10
seconds is a minute. The first number tells
you the maximum number of points you can
get for the question. Assume a question is on
the screen.
5
Demonstrating the point
system
 For math questions there will be a number in
the lower right corner. It will change every
minute. Here I am illustrating with numbers
changing every 10 seconds. Try to imagine 10
seconds is a minute. The first number tells
you the maximum number of points you can
get for the question. Assume a question is on
the screen.
4
Demonstrating the point
system
 For math questions there will be a number in
the lower right corner. It will change every
minute. Here I am illustrating with numbers
changing every 10 seconds. Try to imagine 10
seconds is a minute. The first number tells
you the maximum number of points you can
get for the question. Assume a question is on
the screen.
3
Demonstrating the point
system
 For math questions there will be a number in
the lower right corner. It will change every
minute. Here I am illustrating with numbers
changing every 10 seconds. Try to imagine 10
seconds is a minute. The first number tells
you the maximum number of points you can
get for the question. Assume a question is on
the screen.
2
Demonstrating the point
system
 For math questions there will be a number in
the lower right corner. It will change every
minute. Here I am illustrating with numbers
changing every 10 seconds. Try to imagine 10
seconds is a minute. The first number tells
you the maximum number of points you can
get for the question. Assume a question is on
the screen.
1
TIME’s UP!
THE CHALLENGE BEGINS
VERY IMPORTANT!
Put away all electronic devices; including calculators.
Mechanical devices invented more than a hundred years ago,
are OK.
HQ1. Babylonians
One of the oldest of all known civilizations is
that of the Babylonians, with capital in
Babylon. Where was the city of Babylon
located?
A. In Egypt.
B. In Greece.
C. In Iraq.
D. In Turkey.
E. In Florida.
HQ1. Babylonians
One of the oldest of all known civilizations is
that of the Babylonians, with capital in
Babylon. Where was the city of Babylon
located?
A. In Egypt.
B. In Greece.
C. In Iraq.
D. In Turkey.
E. In Florida.
20 seconds
HQ1. Babylonians
One of the oldest of all known civilizations is
that of the Babylonians, with capital in
Babylon. Where was the city of Babylon
located?
A. In Egypt.
B. In Greece.
C. In Iraq.
D. In Turkey.
E. In Florida.
Time's Up!
HQ1. Babylonians
One of the oldest of all known civilizations is
that of the Babylonians, with capital in
Babylon. Where was the city of Babylon
located?
A. In Egypt.
B. In Greece.
C. In Iraq.
D. In Turkey.
E. In Florida.
Time's Up!
The Babylonians
The name Babylonians is
given to the people living
in the ancient
Mesopotamia, the region
between the rivers Tigris
and Euphrates, modern
day Iraq. They wrote on
clay tablets like the one in
the picture. The civilization
lasted a millennium and a
half, from about 2000 BCE
to 500 BCE.
MQ1-Babylonian Tables
A Babylonian tablet has a table listing n3 +n2 for n = 1
to 30. Here are the first 10 entries of such a table.
Tables as these seem to have been
used to solve cubic equations. Solve
(using the table or otherwise) for an
integer solution.
x  2 x  3136 0.
3
Hint: Set
2
x = 2n.
MQ1-Babylonian Tables
A Babylonian tablet has a table listing n3 +n2 for n = 1
to 30. Here are the first 10 entries of such a table.
Tables as these seem to have been
used to solve cubic equations. Solve
(using the table or otherwise) for an
integer solution.
x  2 x  3136 0.
3
Hint: Set
2
x = 2n.
3
MQ1-Babylonian Tables
A Babylonian tablet has a table listing n3 +n2 for n = 1
to 30. Here are the first 10 entries of such a table.
Tables as these seem to have been
used to solve cubic equations. Solve
(using the table or otherwise) for an
integer solution.
x  2 x  3136 0.
3
Hint: Set
2
x = 2n.
2
MQ1-Babylonian Tables
A Babylonian tablet has a table listing n3 +n2 for n = 1
to 30. Here are the first 10 entries of such a table.
Tables as these seem to have been
used to solve cubic equations. Solve
(using the table or otherwise) for an
integer solution.
x  2 x  3136 0.
3
Hint: Set
2
x = 2n.
1
TIME’s UP!
HQ2. Papyrus Writing
The Rhind or Ahmes papyrus, dated to 1650 BCE is
one of the oldest remaining mathematical
documents. Papyrus is a paper like material made
from
A. Palm leaves
B. Cotton
C. The stems of a water plant.
D. The leaves of a desert lily.
E. Apple peels.
HQ2. Papyrus Writing
The Rhind or Ahmes papyrus, dated to 1650 BCE is
one of the oldest remaining mathematical
documents. Papyrus is a paper like material made
from
A. Palm leaves.
B. Cotton.
C. The stems of a water plant.
D. The leaves of a desert lily.
E. Apple peels.
20 seconds
HQ2. Papyrus Writing
The Rhind or Ahmes papyrus, dated to 1650 BCE is
one of the oldest remaining mathematical
documents. Papyrus is a paper like material made
from
A. Palm leaves.
B. Cotton.
C. The stems of a water plant.
D. The leaves of a desert lily.
E. Apple peels.
Time's Up!
HQ2. Papyrus Writing
The Rhind or Ahmes papyrus, dated to 1650 BCE is
one of the oldest remaining mathematical
documents. Papyrus is a paper like material made
from
A. Palm leaves.
B. Cotton.
C. The stems of a water plant.
D. The leaves of a desert lily.
E. Apple peels.
Papyrus is made from the stems of the papyrus plant, a reed like plant growing
on the shores of the Nile.
MQ2. Solve like an Egyptian
This problem appears in the Rhind
papyrus:
Divide 100 loaves among 5 men in such
a way that the shares received shall be
in arithmetic progression and that one
seventh of the sum of the largest 3
shares shall be equal to the sum of the
smallest two.
All shares but the third (middle) one are
fractions. What is the middle share?
MQ2. Solve like an Egyptian
This problem appears in the Rhind
papyrus:
Divide 100 loaves among 5 men in such
a way that the shares received shall be
in arithmetic progression and that one
seventh of the sum of the largest 3
shares shall be equal to the sum of the
smallest two.
All shares but the third (middle) one are
fractions. What is the middle share?
3
MQ2. Solve like an Egyptian
This problem appears in the Rhind
papyrus:
Divide 100 loaves among 5 men in such
a way that the shares received shall be
in arithmetic progression and that one
seventh of the sum of the largest 3
shares shall be equal to the sum of the
smallest two.
All shares but the third (middle) one are
fractions. What is the middle share?
2
MQ2. Solve like an Egyptian
This problem appears in the Rhind
papyrus:
Divide 100 loaves among 5 men in such
a way that the shares received shall be
in arithmetic progression and that one
seventh of the sum of the largest 3
shares shall be equal to the sum of the
smallest two.
All shares but the third (middle) one are
fractions. What is the middle share?
1
TIME’s UP!
MQ2. Solve like an Egyptian
This problem appears in the Rhind
papyrus:
Divide 100 loaves among 5 men in such
a way that the shares received shall be
in arithmetic progression and that one
seventh of the sum of the largest 3
shares shall be equal to the sum of the
smallest two.
All shares but the third (middle) one are
fractions. What is the middle share?
Answer: 20
HQ3. Pythagoreans
 Hippasus the Pythagorean is said to have
drowned at sea, or suffered some other
punishment for revealing:
A. That there was an infinity of numbers.
B. That some numbers could not be expressed as a
quotient of integers.
C. That every number could be expressed as a
product of primes.
D. That some perfect squares are sums of perfect
squares.
E. That numbers will get you, if you don’t watch
out.
HQ3. Pythagoreans
 Hippasus the Pythagorean is said to have
drowned at sea, or suffered some other
punishment for revealing:
A. That there was an infinity of numbers.
B. That some numbers could not be expressed as a
quotient of integers.
C. That every number could be expressed as a
product of primes.
D. That some perfect squares are sums of perfect
squares.
E. That numbers will get you, if you don’t watch
out.
20 seconds
HQ3. Pythagoreans
 Hippasus the Pythagorean is said to have
drowned at sea, or suffered some other
punishment for revealing:
A. That there was an infinity of numbers.
B. That some numbers could not be expressed as a
quotient of integers.
C. That every number could be expressed as a
product of primes.
D. That some perfect squares are sums of perfect
squares.
E. That numbers will get you, if you don’t watch
out.
Time's Up!
HQ3. Pythagoreans
 Hippasus the Pythagorean is said to have
drowned at sea, or suffered some other
punishment for revealing:
A. That there was an infinity of numbers.
B. That some numbers could not be expressed as a
quotient of integers.
C. That every number could be expressed as a
product of primes.
D. That some perfect squares are sums of perfect
squares.
E. That numbers will get you, if you don’t watch
out.
Time's Up!
More on Pythagoras and his
friends
The Pythagoreans were a secret society flourishing ca. 600-400 BC
They called themselves followers of Pythagoras of Samos, who
may or may not have existed. The most important achievement of
the Pythagoreans was the discovery of irrational numbers,
specifically: The hypotenuse of a right
triangle of legs of length 1 is incommensurable with the legs. Or, as we say now,
the square root of 2 is irrational, cannot be expressed as a ratio of two integers.
The Pythagoreans loved numbers, they adored numbers, they said “Everything
is number.” A property that amazed them was the existence of what they called
amicable or friendly numbers. A pair of numbers m, n is an amicable pair if
each is the sum of the proper divisors of the other one.
Pythagoras and his friends
Their only example was the pair 220, 284.
The proper divisors of 220 are: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110.
1+2+4+5+10+11+20+22+44+55+110 = 284.
The proper divisors of 284 are: 1, 2, 4, 71, 142.
1+2+4+71+142 = 220.
MQ3. Looking for Friends
It is known that
1184
is a member of an amicable pair.
It is feeling lonely. Find its friend.
MQ3. Looking for Friends
It is known that
1184
is a member of an amicable pair.
It is feeling lonely. Find its friend.
4
MQ3. Looking for Friends
It is known that
1184
is a member of an amicable pair.
It is feeling lonely. Find its friend.
3
MQ3. Looking for Friends
It is known that
1184
is a member of an amicable pair.
It is feeling lonely. Find its friend.
2
MQ3. Looking for Friends
It is known that
1184
is a member of an amicable pair.
It is feeling lonely. Find its friend.
1
TIME’s UP!
The answer is 1210
 To find the divisors of 1184 we can start
seeing that it is even, see how many powers
of 2 divide it. 1184/2 = 592, 592/2 = 296,
296/2 = 148, 148/2 = 74, 74/2 = 37, and 37 is
prime. That is: 1184 = 25●37. The divisors are
all of the form 2p and 2p ●37, 0 ≤ p ≤ 5:
1, 2, 4, 8, 16, 32, 1 37  37, 2  37  74,
4  37  148, 8  37  296, 16 37  592
1+2+4+8+16+32+37+74+148+296+592 = 1210
HQ4. The invention of
nothing
The number 0 in its modern form, and the
concept of a negative number first appears in:
A. India.
B. Greece.
C. Rome.
D. Egypt.
E. China.
HQ4. The invention of
nothing
The number 0 in its modern form, and the
concept of a negative number first appears in:
A. India.
B. Greece.
C. Rome.
D. Egypt.
E. China.
20 seconds
HQ . The invention of
nothing
The number 0 in its modern form, and the
concept of a negative number first appears in:
A. India.
B. Greece.
C. Rome.
D. Egypt.
E. China.
Time’s Up!
HQ . The invention of
nothing
The number 0 in its modern form, and the
concept of a negative number first appears in:
A. India.
B. Greece.
C. Rome.
D. Egypt.
E. China.
Time’s Up!
MQ4. Brahmagupta’s legacy
A quadrilateral of sides of lenghts 4, 5, 7, and 10, is inscribed
in a circle. The radius of the circle can be expressed in the
form R  mn s where m, n, s are positive integers,
the greatest common divisor of m and n is 1, and s is
square free. Determine m + n + s
MQ4. Brahmagupta’s legacy
A quadrilateral of sides of lenghts 4, 5, 7, and 10, is inscribed
in a circle. The radius of the circle can be expressed in the
form R  mn s where m, n, s are positive integers,
the greatest common divisor of m and n is 1, and s is
square free. Determine m + n + s
3
MQ4. Brahmagupta’s legacy
A quadrilateral of sides of lenghts 4, 5, 7, and 10, is inscribed
in a circle. The radius of the circle can be expressed in the
form R  mn s where m, n, s are positive integers,
the greatest common divisor of m and n is 1, and s is
square free. Determine m + n + s
2
MQ4. Brahmagupta’s legacy
A quadrilateral of sides of lenghts 4, 5, 7, and 10, is inscribed
in a circle. The radius of the circle can be expressed in the
form R  mn s where m, n, s are positive integers,
the greatest common divisor of m and n is 1, and s is
square free. Determine m + n + s
1
TIME’s UP!
MQ4. Brahmagupta’s legacy
A quadrilateral of sides of lenghts 4, 5, 7, and 10, is inscribed
in a circle. The radius of the circle can be expressed in the
form R  mn s where m, n, s are positive integers,
the greatest common divisor of m and n is 1, and s is
square free. Determine m + n + s
The answer is 78
HQ5. Fibonacci’s rabbits
The title of the book in which Fibonacci has the
famous rabbit problem, solved by the famous
Fibonacci sequence is
A.
B.
C.
D.
E.
The book of numbers.
The book of the golden mean.
The book of calculations.
The book of sums.
Peter Rabbit and family.
HQ5. Fibonacci’s rabbits
The title of the book in which Fibonacci has the
famous rabbit problem, solved by the famous
Fibonacci sequence is
A.
B.
C.
D.
E.
The book of numbers.
The book of the golden mean.
The book of calculations.
The book of sums.
Peter Rabbit and family.
20 seconds
HQ5. Fibonacci’s rabbits
The title of the book in which Fibonacci has the
famous rabbit problem, solved by the famous
Fibonacci sequence is
A.
B.
C.
D.
E.
The book of numbers.
The book of the golden mean.
The book of calculations.
The book of sums.
Peter Rabbit and family.
Time’s Up!
HQ5. Fibonacci’s rabbits
The title of the book in which Fibonacci has the
famous rabbit problem, solved by the famous
Fibonacci sequence is
A.
B.
C.
D.
E.
The book of numbers.
The book of the golden mean.
The book of calculations.
The book of sums.
Peter Rabbit and family.
MQ5. Recurrence
The Fibonacci sequence is an example of a
sequence defined recursively. Here is another
example. The sequence of numbers
a0 , a 1 , a 2 , a 3 , a 4 , . . .
satisfies: an  5an1  6an2 if n ≥ 2. If
a0 = 3 and a5 = 307, what is a1 ?
MQ5. Recurrence
The Fibonacci sequence is an example of a
sequence defined recursively. Here is another
example. The sequence of numbers
a0 , a 1 , a 2 , a 3 , a 4 , . . .
satisfies: an  5an1  6an2 if n ≥ 2. If
a0 = 3 and a5 = 307, what is a1 ?
4
MQ5. Recurrence
The Fibonacci sequence is an example of a
sequence defined recursively. Here is another
example. The sequence of numbers
a0 , a 1 , a 2 , a 3 , a 4 , . . .
satisfies: an  5an1  6an2 if n ≥ 2. If
a0 = 3 and a5 = 307, what is a1 ?
3
MQ5. Recurrence
The Fibonacci sequence is an example of a
sequence defined recursively. Here is another
example. The sequence of numbers
a0 , a 1 , a 2 , a 3 , a 4 , . . .
satisfies: an  5an1  6an2 if n ≥ 2. If
a0 = 3 and a5 = 307, what is a1 ?
2
MQ5. Recurrence
The Fibonacci sequence is an example of a
sequence defined recursively. Here is another
example. The sequence of numbers
a0 , a 1 , a 2 , a 3 , a 4 , . . .
satisfies: an  5an1  6an2 if n ≥ 2. If
a0 = 3 and a5 = 307, what is a1 ?
1
TIME’s UP!
MQ5. Recurrence
The Fibonacci sequence is an example of a
sequence defined recursively. Here is another
example. The sequence of numbers
a0 , a 1 , a 2 , a 3 , a 4 , . . .
satisfies: an  5an1  6an2 if n ≥ 2. If
a0 = 3 and a5 = 307, what is a1 ?
The answer is 7
MQ5. Recurrence
The sequence of numbers
a0 , a1 , a2 , a3 , a4 , . . . satisfies: an  5an1  6an2
if n ≥ 2. If a0 = 3 and a5 = 307, what is a1 ?
HQ6. Talking of Fibonacci
One of the main purposes of Fibonacci’s book
was
A. To discuss sequences and show how they
can be used.
B. To introduce the Arabic numerals to Europe.
C. To introduce new techniques for solving
equations.
D. To discuss the logarithmic spiral and its
applications.
E. To warn people about the danger of
breeding rabbits.
Leonardo Pisano
(1170-1250)
HQ6. Talking of Fibonacci
One of the main purposes of Fibonacci’s book
was
A. To discuss sequences and show how they
can be used.
B. To introduce the Arabic numerals to Europe.
C. To introduce new techniques for solving
equations.
D. To discuss the logarithmic spiral and its
applications.
E. To warn people about the danger of
breeding rabbits.
Leonardo Pisano
(1170-1250)
20 seconds
HQ6. Talking of Fibonacci
One of the main purposes of Fibonacci’s book
was
A. To discuss sequences and show how they
can be used.
B. To introduce the Arabic numerals to Europe.
C. To introduce new techniques for solving
equations.
D. To discuss the logarithmic spiral and its
applications.
E. To warn people about the danger of
breeding rabbits.
Leonardo Pisano
(1170-1250)
Time’s Up
HQ6. Talking of Fibonacci
One of the main purposes of Fibonacci’s book
was
A. To discuss sequences and show how they
can be used.
B. To introduce the Arabic numerals to Europe.
C. To introduce new techniques for solving
equations.
Liber Abaci begins with:
``The nine Indian figures are:
9 8 7 6 5 4 3 2 1:
With these nine figures and with sign 0 which
the Arabs call zephir any number whatsoever
is written, as is demonstrated below.’’
Leonardo Pisano
(1170-1250)
HQ7. Donkeys Crossing
The fifth proposition in the first volume of
Euclid’s elements was known as the
``pons asinorum,’’ ``bridge of asses.’’ It
states
A. If in a triangle two angles equal each
other, then the triangle is isosceles.
B. In an isosceles triangle, the base angles
are equal.
C. In any triangle the sum of any two sides
is greater then the remaining side
D. In any triangle the sum of the three
interior angles of the triangle equals
two right angles.
E. In any triangle, the side opposite the
greater angle is greater.
HQ7. Donkeys Crossing
The fifth proposition in the first volume of
Euclid’s elements was known as the
``pons asinorum,’’ ``bridge of asses.’’ It
states
A. If in a triangle two angles equal each
other, then the triangle is isosceles.
B. In an isosceles triangle, the base angles
are equal.
C. In any triangle the sum of any two sides
is greater then the remaining side
D. In any triangle the sum of the three
interior angles of the triangle equals
two right angles.
E. In any triangle, the side opposite the
greater angle is greater.
20 seconds
HQ7. Donkeys Crossing
The fifth proposition in the first volume of
Euclid’s elements was known as the
``pons asinorum,’’ ``bridge of asses.’’ It
states
A. If in a triangle two angles equal each
other, then the triangle is isosceles.
B. In an isosceles triangle, the base angles
are equal.
C. In any triangle the sum of any two sides
is greater then the remaining side
D. In any triangle the sum of the three
interior angles of the triangle equals
two right angles.
E. In any triangle, the side opposite the
greater angle is greater.
Time's Up!
HQ7. Donkeys Crossing
The fifth proposition in the first volume of
Euclid’s elements was known as the
``pons asinorum,’’ ``bridge of asses.’’ It
states
A. If in a triangle two angles equal each
other, then the triangle is isosceles.
B. In an isosceles triangle, the base angles
are equal.
C. In any triangle the sum of any two sides
is greater then the remaining side
D. In any triangle the sum of the three
interior angles of the triangle equals
two right angles.
E. In any triangle, the side opposite the
greater angle is greater.
MQ6. Circles
 Let R be the radius of the circumscribed, r the
radius of the inscribed circle of a triangle of sides
21, 20, 13. The ratio R/r can be expressed as a ratio
of two positive integers a, b with no common
divisors other than 1. Find a + b.: R/r = a/b,
gcd(a,b)=1. What is a+b ? Possible hint: 21 = 5+16
MQ6. Circles
 Let R be the radius of the circumscribed, r the
radius of the inscribed circle of a triangle of sides
21, 20, 13. The ratio R/r can be expressed as a ratio
of two positive integers a, b with no common
divisors other than 1: R/r = a/b, gcd(a,b)=1. What is
a+b ? Possible hint: 21 = 5+16
3
MQ6. Circles
 Let R be the radius of the circumscribed, r the
radius of the inscribed circle of a triangle of sides
21, 20, 13. The ratio R/r can be expressed as a ratio
of two positive integers a, b with no common
divisors other than 1: R/r = a/b, gcd(a,b)=1. What is
a+b ? Possible hint: 21 = 5+16
2
MQ6. Circles
 Let R be the radius of the circumscribed, r the
radius of the inscribed circle of a triangle of sides
21, 20, 13. The ratio R/r can be expressed as a ratio
of two positive integers a, b with no common
divisors other than 1: R/r = a/b, gcd(a,b)=1. What is
a+b ? Possible hint: 21 = 5+16
1
TIME’s UP!
MQ6. Circles
 Let R be the radius of the circumscribed, r the
radius of the inscribed circle of a triangle of sides
21, 20, 13. The ratio R/r can be expressed as a ratio
of two positive integers a, b with no common
divisors other than 1: R/r = a/b, gcd(a,b)=1. What is
a+b ? Possible hint: 21 = 5+16
The answer is
93
HQ8. The Word Became Number
The inventor of logarithms was
A. An Italian priest.
B. A Greek mathematician.
C. A Scottish nobleman.
D. A German philosopher.
E. A Chinese mathematician
HQ8. The Word Became Number
The inventor of logarithms was
A. An Italian priest.
B. A Greek mathematician.
C. A Scottish nobleman.
D. A German philosopher.
E. A Chinese mathematician
20 seconds
HQ8. The Word Became Number
The inventor of logarithms was
A. An Italian priest.
B. A Greek mathematician.
C. A Scottish nobleman.
D. A German philosopher.
E. A Chinese mathematician
Time's Up!
HQ8. The Word Became Number
The inventor of logarithms was
A. An Italian priest.
B. A Greek mathematician.
C. A Scottish nobleman.
D. A German philosopher.
E. A Chinese mathematician
John Napier
(1550-1617)
Time's Up!
MQ7. Logarithms
 With log being logarithm in base 10,
compute
log 2 + log 4 + log 8 + log 25 + log 625
MQ7. Logarithms
 With log being logarithm in base 10,
compute
log 2 + log 4 + log 8 + log 25 + log 625
2
MQ7. Logarithms
 With log being logarithm in base 10,
compute
log 2 + log 4 + log 8 + log 25 + log 625
1
TIME’s UP!
MQ7. Logarithms
 With log being logarithm in base 10,
compute
log 2 + log 4 + log 8 + log 25 + log 625 =
log (2×4×8×25×625) = log(106) = 6.
The answer is 6.
HQ9.The Renaissance
Rafael Bombelli was one of the leading
mathematicians of the 16th century. He was
born in the city whose university, founded
1088, may be the oldest in the world. That
city is
A.
B.
C.
D.
E.
Rome
Venice
Pisa
Florence
Bologna
HQ9.The Renaissance
Rafael Bombelli was one of the leading
mathematicians of the 16th century. He was
born in the city whose university, founded
1088, may be the oldest in the world. That
city is
A.
B.
C.
D.
E.
Rome
Venice
Pisa
Florence
Bologna
20 seconds
HQ9.The Renaissance
Rafael Bombelli was one of the leading
mathematicians of the 16th century. He was
born in the city whose university, founded
1088, may be the oldest in the world. That
city is
A.
B.
C.
D.
E.
Rome
Venice
Pisa
Florence
Bologna
Time’s Up
HQ9.The Renaissance
Rafael Bombelli was one of the leading
mathematicians of the 16th century. He was
born in the city whose university, founded
1088, may be the oldest in the world. That
city is
A.
B.
C.
D.
E.
Rome
Venice
Pisa
Florence
Bologna
Time’s Up
MQ8. From Bombelli’s Algebra
A square is inscribed in triangle ABC
with one side on BC.
If |AB| = 13, |BC| = 14, |CA| = 15, the
length of the side of the square has
the form a/b, where a, b are positive
integers with no common divisor
other than 1. Find a + b.
MQ8. From Bombelli’s Algebra
A square is inscribed in triangle ABC
with one side on BC.
If |AB| = 13, |BC| = 14, |CA| = 15, the
length of the side of the square has
the form a/b, where a, b are positive
integers with no common divisor
other than 1. Find a + b.
5
MQ8. From Bombelli’s Algebra
A square is inscribed in triangle ABC
with one side on BC.
If |AB| = 13, |BC| = 14, |CA| = 15, the
length of the side of the square has
the form a/b, where a, b are positive
integers with no common divisor
other than 1. Find a + b.
4
MQ8. From Bombelli’s Algebra
A square is inscribed in triangle ABC
with one side on BC.
If |AB| = 13, |BC| = 14, |CA| = 15, the
length of the side of the square has
the form a/b, where a, b are positive
integers with no common divisor
other than 1. Find a + b.
3
MQ8. From Bombelli’s Algebra
A square is inscribed in triangle ABC
with one side on BC.
If |AB| = 13, |BC| = 14, |CA| = 15, the
length of the side of the square has
the form a/b, where a, b are positive
integers with no common divisor
other than 1. Find a + b.
2
MQ8. From Bombelli’s Algebra
A square is inscribed in triangle ABC
with one side on BC.
If |AB| = 13, |BC| = 14, |CA| = 15, the
length of the side of the square has
the form a/b, where a, b are positive
integers with no common divisor
other than 1. Find a + b.
1
TIME’s UP!
MQ8. From Bombelli’s Algebra
A square is inscribed in triangle ABC
with one side on BC.
If |AB| = 13, |BC| = 14, |CA| = 15, the
length of the side of the square has
the form a/b, where a, b are positive
integers with no common divisor
other than 1. Find a + b.
The answer is 97
HQ10. Mathematical Advances
Who said “Standard mathematics has recently been rendered obsolete
by the discovery that for years we have been writing the numeral
five backward. This has led to reevaluation of counting as a method
of getting from one to ten. Students are taught advanced concepts
of Boolean algebra, and formerly unsolvable equations are dealt
with by threats of reprisals”
A.
Woody Allen.
B.
Jon Stewart.
C.
Stephen Colbert.
D. Lord Bertrand Russell.
E.
Stephen Hawking.
HQ10. Mathematical Advances
Who said “Standard mathematics has recently been rendered obsolete
by the discovery that for years we have been writing the numeral
five backward. This has led to reevaluation of counting as a method
of getting from one to ten. Students are taught advanced concepts
of Boolean algebra, and formerly unsolvable equations are dealt
with by threats of reprisals”
A.
Woody Allen.
B.
Jon Stewart.
C.
Stephen Colbert.
D. Lord Bertrand Russell.
E.
Stephen Hawking.
20 seconds
HQ10. Mathematical Advances
Who said “Standard mathematics has recently been rendered obsolete
by the discovery that for years we have been writing the numeral
five backward. This has led to reevaluation of counting as a method
of getting from one to ten. Students are taught advanced concepts
of Boolean algebra, and formerly unsolvable equations are dealt
with by threats of reprisals”
A.
Woody Allen.
B.
Jon Stewart.
C.
Stephen Colbert.
D. Lord Bertrand Russell.
E.
Stephen Hawking.
Time's Up!
HQ10. Mathematical Advances
Who said “Standard mathematics has recently been rendered obsolete
by the discovery that for years we have been writing the numeral
five backward. This has led to reevaluation of counting as a method
of getting from one to ten. Students are taught advanced concepts
of Boolean algebra, and formerly unsolvable equations are dealt
with by threats of reprisals”
A.
Woody Allen.
B.
Jon Stewart.
C.
Stephen Colbert.
D. Lord Bertrand Russell.
E.
Stephen Hawking.
Time's Up!
HQ11. Back to the
Pythagoreans
Which of the following was NOT a
rule the Pythagoreans had to follow:
A. Don’t eat beans.
B. Never stir the fire with a knife.
C. Touch the earth when it thunders.
D. Spit on your nail pairings and hair
trimmings.
E. No women are allowed at the
meetings.
HQ11. Back to the
Pythagoreans
Which of the following was NOT a
rule the Pythagoreans had to follow:
A. Don’t eat beans.
B. Never stir the fire with a knife.
C. Touch the earth when it thunders.
D. Spit on your nail pairings and hair
trimmings.
E. No women are allowed at the
meetings.
20 seconds
HQ11. Back to the
Pythagoreans
Which of the following was NOT a
rule the Pythagoreans had to follow:
A. Don’t eat beans.
B. Never stir the fire with a knife.
C. Touch the earth when it thunders.
D. Spit on your nail pairings and hair
trimmings.
E. No women are allowed at the
meetings.
Time's Up!
HQ11. Back to the
Pythagoreans
Which of the following was NOT a
rule the Pythagoreans had to follow:
A. Don’t eat beans.
B. Never stir the fire with a knife.
C. Touch the earth when it thunders.
D. Spit on your nail pairings and hair
trimmings.
E. No women are allowed at the
meetings.
Time's Up!
HQ12.
Euler
 Leonhard Euler (1707-1783) was the greatest
mathematician of the 18th century and one of
the greatest of all times. He was born in
A. Basel, Switzerland.
B. Berlin, Germany.
C. Bonn, Germany.
D. Salzburg, Austria.
E. Vienna, Austria.
HQ12.
Euler
 Leonhard Euler (1707-1783) was the greatest
mathematician of the 18th century and one of
the greatest of all times. He was born in
A. Basel, Switzerland.
B. Berlin, Germany.
C. Bonn, Germany.
D. Salzburg, Austria.
E. Vienna, Austria.
20 seconds
HQ12.
Euler
 Leonhard Euler (1707-1783) was the greatest
mathematician of the 18th century and one of
the greatest of all times. He was born in
A. Basel, Switzerland.
B. Berlin, Germany.
C. Bonn, Germany.
D. Salzburg, Austria.
E. Vienna, Austria.
Time’s Up!
HQ12.
Euler
 Leonhard Euler (1707-1783) was the greatest
mathematician of the 18th century and one of
the greatest of all times. He was born in
A. Basel, Switzerland.
B. Berlin, Germany.
C. Bonn, Germany.
D. Salzburg, Austria.
E. Vienna, Austria.
Time’s Up!
HQ13. Etymologies
 The word algebra is
A. Of Greek origin.
B. Of Arabic origin.
C. Of Indian origin.
D. Of Latin origin.
E. Of Italian origin.
HQ13. Etymologies
 The word algebra is
A. Of Greek origin.
B. Of Arabic origin.
C. Of Indian origin.
D. Of Latin origin.
E. Of Italian origin.
10 seconds
HQ13. Etymologies
 The word algebra is
A. Of Greek origin.
B. Of Arabic origin.
C. Of Indian origin.
D. Of Latin origin.
E. Of Italian origin.
Times Up
HQ13. Etymologies
 The word algebra is
A. Of Greek origin.
B. Of Arabic origin.
C. Of Indian origin.
D. Of Latin origin.
E. Of Italian origin.
HQ14. Women in mathematics
She was one of the very important mathematicians
of the 20th century, making essential
contributions to both abstract algebra and
physics. She was recently the subject of a long
article in the New York Times. Her name is
A. Frances Langford.
B. Matilda Neuberger.
C. Lise Meitner.
D. Anne Dubreil.
E. Emmy Noether.
HQ14. Women in mathematics
She was one of the very important mathematicians
of the 20th century, making essential
contributions to both abstract algebra and
physics. She was recently the subject of a long
article in the New York Times. Her name is
A. Frances Langford.
B. Matilda Neuberger.
C. Lise Meitner.
D. Anne Dubreil.
E. Emmy Noether.
10 seconds
HQ14. Women in mathematics
She was one of the very important mathematicians
of the 20th century, making essential
contributions to both abstract algebra and
physics. She was recently the subject of a long
article in the New York Times. Her name is
A. Frances Langford.
B. Matilda Neuberger.
C. Lise Meitner.
D. Anne Dubreil.
E. Emmy Noether.
Time’s Up!
HQ14. Women in mathematics
She was one of the very important mathematicians
of the 20th century, making essential
contributions to both abstract algebra and
physics. She was recently the subject of a long
article in the New York Times. Her name is
A. Frances Langford.
B. Matilda Neuberger.
C. Lise Meitner.
D. Anne Dubreil.
E. Emmy Noether.
Time’s Up!
HQ15. A French nobleman.
 The Marquis of L’Hôpital (1661-1704) was the
author of the very first Calculus textbook. His
famous rule appears in it. But it seems the
book was really written by:
A. Isaak Newton.
B. Johan Bernoulli.
C. Gottfried Leibniz.
D. Isaak Barrow.
E. Abraham DeMoivre.
HQ15. A French nobleman.
 The Marquis of L’Hôpital (1661-1704) was the
author of the very first Calculus textbook. His
famous rule appears in it. But it seems the
book was really written by:
A. Isaak Newton.
B. Johan Bernoulli.
C. Gottfried Leibniz.
D. Isaak Barrow.
E. Abraham DeMoivre.
10 seconds
HQ15. A French nobleman.
 The Marquis of L’Hôpital (1661-1704) was the
author of the very first Calculus textbook. His
famous rule appears in it. But it seems the
book was really written by:
A. Isaak Newton.
B. Johan Bernoulli.
C. Gottfried Leibniz.
D. Isaak Barrow.
E. Abraham DeMoivre.
Time’s Up!
HQ15. A French nobleman.
 The Marquis of L’Hôpital (1661-1704) was the
author of the very first Calculus textbook. His
famous rule appears in it. But it seems the
book was really written by:
A. Isaak Newton.
B. Johan Bernoulli.
C. Gottfried Leibniz.
D. Isaak Barrow.
E. Abraham DeMoivre.
Time’s Up!
HQ16. Conjectures.
 The Goldbach conjecture states:
A. Every even integer greater than 4 is a sum of
two primes.
B. There exists an infinity of primes p such that
p+2 is also prime.
C. There exists an infinity of primes of the form
5k+7, where k is a positive integer.
D. If 2p – 1 is prime, then p is prime.
E. An infinite number of Fibonacci numbers are
prime.
HQ16. Conjectures.
 The Goldbach conjecture states:
A. Every even integer greater than 4 is a sum of
two primes.
B. There exists an infinity of primes p such that
p+2 is also prime.
C. There exists an infinity of primes of the form
5k+7, where k is a positive integer.
D. If 2p – 1 is prime, then p is prime.
E. An infinite number of Fibonacci numbers are
prime.
10 seconds
HQ16. Conjectures.
 The Goldbach conjecture states:
A. Every even integer greater than 4 is a sum of
two primes.
B. There exists an infinity of primes p such that
p+2 is also prime.
C. There exists an infinity of primes of the form
5k+7, where k is a positive integer.
D. If 2p – 1 is prime, then p is prime.
E. An infinite number of Fibonacci numbers are
prime.
Time’s Up!
HQ16. Conjectures.
 The Goldbach conjecture states:
A. Every even integer greater than 4 is a sum of
two primes.
B. There exists an infinity of primes p such that
p+2 is also prime.
C. There exists an infinity of primes of the form
5k+7, where k is a positive integer.
D. If 2p – 1 is prime, then p is prime.
E. An infinite number of Fibonacci numbers are
prime.