How many seconds in 11 years?

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(No Transcript)
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• How many seconds in 11 years?

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• How many seconds in 11 years?
• Ans. 346,896,000

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• How many seconds in 11 years?
• Ans. 346,896,000
• Less than 4 seconds by a 7 year old

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• What is the square root of 106,929?

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• What is the square root of 106,929?
• Ans. 327

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• What is the square root of 106,929?
• Ans. 327
• 4 seconds by 8 year old

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• Find the number whose cube less 19 multiplied by
  its cube shall be equal to the cube of 6.

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• Find the number whose cube less 19 multiplied by
  its cube shall be equal to the cube of 6.
• Ans. 3
• 2 seconds by 13 year old

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• Find the number whose cube less 19 multiplied by
  its cube shall be equal to the cube of 6.
• Ans. 3
• 2 seconds by 13 year old

• (3³-19) x 3³ 6³

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Child Prodigy
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Child Prodigy

• is someone who is a master of one or more skills
  or arts at an early age.

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Child Prodigy

• is someone who is a master of one or more skills
  or arts at an early age.
• someone who by the age 11 displays expert
  proficiency or a profound grasp of the
  fundamentals in a field usually only undertaken
  by adults.

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Famous Math ProdigiesGalois, Euler, Gauss, Pascal
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Zerah Colburn (1804-1840)

• Born the fifth of seven children.
• Parents were farmers in Vermont
• Born with six digits on both hands and both feet.
• The supernumerary digits had been in the family
  for four generations.
• With very little schooling and not being able to
  read or write, Zerah at the age of 6 began
  repeating the multiplication tables to himself.
• Zerah began performing in public exhibitions at
  the age of 6.

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Zerah Colburn (1804-1840)

• Questions performed
• Admitting the distance between Concord and Boston
  to be 65 miles, how many steps must I take in
  going this distance, allowing that I go three
  feet at a step?

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Zerah Colburn (1804-1840)

• Questions performed
• Admitting the distance between Concord and Boston
  to be 65 miles, how many steps must I take in
  going this distance, allowing that I go three
  feet at a step?
• The answer of 114,400 was given in 10 seconds.

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Zerah Colburn (1804-1840)

• How many days and hours since the Christian era
  commenced, 1811 years (Zerah usually assumed a
  365-day year and a 30-day month)?

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Zerah Colburn (1804-1840)

• How many days and hours since the Christian era
  commenced, 1811 years (Zerah usually assumed a
  365-day year and a 30-day month)?
• Answered in 20 seconds
• 661,015 days and 15,864,360 hours.

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Zerah Colburn (1804-1840)

• When asked which two numbers multiplied together
  produce 1242, Zerah gave answers as fast as he
  could say them

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Zerah Colburn (1804-1840)

• When asked which two numbers multiplied together
  produce 1242, Zerah gave answers as fast as he
  could say them
• 54 and 23, 9 and 138, 3 and 414, 6 and 207,
• 27 and 46, 2 and 621.

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Zerah Colburn

• After his fathers passing in December 1822,
  Zerah returned home and pursued a simple life.
  The rest of his days would see him make
  astronomical calculations for observatories,
  engage in ministerial duties, and teach modern
  and classical languages and literature. On March
  2, 1840, the Reverend Zerah Colburn died, a
  husband and father of three daughters.

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George Parker Bidder (1806-1878)

• Born on June 14, 1806, to a stonemason in
  Moreton Hampstead, England.
• When Bidder was enrolled at the village school at
  the age of six, he found that it was not much to
  his taste.
• Bidder began to teach himself to count fives and
  tens and then set about to learn the
  multiplication table with the use of marbles and
  peas.

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George Parker Bidder

• His early days saw Bidder spend many hours with a
  local blacksmith.
• As the months passed, Bidder still had not
  received any formal instruction. While working
  with the blacksmith, Bidder would be given new
  ideas from people who would come to test his
  powers. People would continually encourage Bidder
  to improve and master his peculiar faculty until
  the time when his talent was almost incredible.
• At the age of 10, Bidder reached a point where he
  could multiply 12 places of figures with 12
  figures.
• Bidders father soon saw the financial promise
  that his sons talent could generate. Withdrawing
  him from school, Bidders father took his son
  about the country for the purpose of exhibition.

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George Parker Bidder

• Here are some typical questions put to and
  answered by
• Bidder in his exhibitions during the years
  1815-1819.
• If the moon be distant from the Earth 123,256
  miles and sound travels at a rate of 4 miles per
  minute, how long would it be before the
  inhabitants of the moon could hear of the battle
  of Waterloo?

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George Parker Bidder

• Here are some typical questions put to and
  answered by Bidder in his exhibitions during the
  years 1815-1819.
• If the moon be distant from the Earth 123,256
  miles and sound travels at a rate of 4 miles per
  minute, how long would it be before the
  inhabitants of the moon could hear of the battle
  of Waterloo?
• Ans. 2 days, 9 hrs and 34 min in less than a
  minute.

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George Parker Bidder

• If the pendulum of a clock vibrates the distance
  of 9¾ inches in a second of time, how many inches
  will it vibrate in 7 years, 14 days, 2 hours, 1
  minute and 56 seconds?

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George Parker Bidder

• If the pendulum of a clock vibrates the distance
  of 9¾ inches in a second of time, how many inches
  will it vibrate in 7 years, 14 days, 2 hours, 1
  minute and 56 seconds?
• With each year being 365 days, 5 hours, 48
  minutes and 55 seconds,
• the answer, in less than a minute, was
  2,165,625,744 ¾ inches.

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George Parker Bidder

• If the globe is 24,912 miles in circumference,
  and a balloon travels 3,878 feet in a minute, how
  long would it be in travelling round the world?

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George Parker Bidder

• If the globe is 24,912 miles in circumference,
  and a balloon travels 3,878 feet in a minute, how
  long would it be in travelling round the world?
• Ans. in 2 minutes 23 days, 13 hours, 18 min

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George Parker Bidder

• Accomplishments
• Played a significant role in the construction of
  Norways first railway.
• Served as engineer-in-chief of the Royal Danish
  railway.
• Advisor for the Metropolitan Board of London
  regarding draining and purification of the river
  Thames.
• Of all his accomplishments and endeavours, Bidder
  is most known for his construction and
  development of the Victoria Docks.
• When one thinks of the early nineteenth century,
  during the time of great engineering
  accomplishments, one must not overlook one of the
  foremost engineers of the time, George Parker
  Bidder.

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• Up until the last days of his life, Bidder had
  retained his calculating abilities. When in
  conversation with his friend, a query was
  suggested that if the speed of light was 190,000
  mi/s, and the wavelength of the red rays at
  36,918 to an inch, how many of its waves must
  strike the eye in one second? As his friend takes
  out a pencil in an attempt to write out the
  calculations, Bidder says You need not work it
  outthe number of vibrations will be
  444,433,651,200,000.
• Two days later, on September 28, 1878, George
  Parker Bidder died.

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• He is probably the most outstanding mental
  calculator of all peoples and all time.

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• He is probably the most outstanding mental
  calculator of all peoples and all time.
• Johann Dase was the one who uttered these words,
  and of the person he was referring to

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Johann Dase (1824-1861)

• He is probably the most outstanding mental
  calculator of all peoples and all time.
• Johann Dase was the one who uttered these words,
  and of the person he was referring to
• he was referring to himself.

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Johann Dase (1824-1861)

• Born in Hamburg, Germany on June 23, 1824, the
  son of a distiller.
• Very little is known of Dases ancestry. As for
  Dase himself, he began schooling at the age of
  two and a half years.
• Although he began at an early age, Dase
  attributes his ability to later practice and not
  his early instruction.

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Johann Dase (1824-1861)

• At the age of 15, Dase began travelling through
  Germany, Denmark and England performing in public
  exhibitions.
• In 1840, while in Vienna, Dase was introduced to
  scientific work. Under the guidance of a
  mathematics professor, Dase was shown how to
  compute p. Having worked on this problem for
  nearly two months, Dase had successfully computed
  p to 205 places.

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Johann Dase (1824-1861)

• What could Dase do?

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Johann Dase (1824-1861)

• What could Dase do?
• Dase was able to count at a glance the number of
  peas thrown on a table and instantly added the
  spots on a group of dominoes.

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Johann Dase (1824-1861)

• What could Dase do?
• Dase was able to count at a glance the number of
  peas thrown on a table and instantly added the
  spots on a group of dominoes.
• He could multiply mentally two numbers each of
  twenty figures in 6 min of forty figures in 40
  min and one hundred figures in 8 hours.

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Johann Dase (1824-1861)

• What could Dase do?
• Dase was able to count at a glance the number of
  peas thrown on a table and instantly added the
  spots on a group of dominoes.
• He could multiply mentally two numbers each of
  twenty figures in 6 min of forty figures in 40
  min and one hundred figures in 8 hours.
• He extracted mentally the square root of a number
  of 100 figures in 52 minutes.

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Johann Dase (1824-1861)

• When the number 935,173,853,927 was given, Dase
  was proficient enough to repeat it forwards and
  backwards after just glancing at it for a mere
  second.
• Dase had offered to multiply this number by any
  number offered. When 7 was chosen, Dase
  immediately replied 6,546,216,977,489. An hour
  later, just before he was to depart from his
  exhibition, Dase was asked if he could still
  recall the number that was discussed earlier.
  Dase instantaneously repeated the number forward
  and backward.

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Johann Dase (1824-1861)

• Dase passed away in 1861 at the age of 37.
• What can be said about Dase is that he
  desperately desired to produce something of value
  for the mathematics and science community.
• In the end, all that this math prodigy wished
  for was to leave his mark on the world.

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Jacques Inaudi (1867-1950)

• Born to a poor Italian family on October 13,
  1867.
• Spent most of his early youth tending to sheep.
• At the age of 6, began to calculate in an attempt
  to compensate for his boredom while attending to
  the livestock.
• By the age of 7, Inaudi was able to multiply 5
  figures by 5 figures. With such a special talent
  having been discovered, Inaudi and his elder
  brother travelled to many major cities across
  Europe demonstrating his abilities in public
  exhibitions.

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions
• 1. a subtraction involving two 21-digit numbers

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions
• 1. a subtraction involving two 21-digit numbers
• 2. the addition of five numbers of 6 digits each

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions
• 1. a subtraction involving two 21-digit numbers
• 2. the addition of five numbers of 6 digits each
• 3. squaring a 4-digit number

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions
• 1. a subtraction involving two 21-digit numbers
• 2. the addition of five numbers of 6 digits each
• 3. squaring a 4-digit number
• 4. a division (the size of the numbers are not
  specified)

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions
• 1. a subtraction involving two 21-digit numbers
• 2. the addition of five numbers of 6 digits each
• 3. squaring a 4-digit number
• 4. a division (the size of the numbers are not
  specified)
• 5. the cube root of a 9-digit number

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions
• 1. a subtraction involving two 21-digit numbers
• 2. the addition of five numbers of 6 digits each
• 3. squaring a 4-digit number
• 4. a division (the size of the numbers are not
  specified)
• 5. the cube root of a 9-digit number
• 6. the fifth root of a 12-digit number

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Jacques Inaudi (1867-1950)

• Inaudis exhibition program consisted of 6
  questions
• 1. a subtraction involving two 21-digit numbers
• 2. the addition of five numbers of 6 digits each
• 3. squaring a 4-digit number
• 4. a division (the size of the numbers are not
  specified)
• 5. the cube root of a 9-digit number
• 6. the fifth root of a 12-digit number
• plus a few questions which asks him to find
  which day of the week a date falls on. (e.g.,
  October 5, 1888 Friday)

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Jacques Inaudi (1867-1950)

• When asked to find a two digit number such that
  the difference between 4 times the first digit
  and three times the second is seven and that when
  reversed is the number reduced by 18

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Jacques Inaudi (1867-1950)

• When asked to find a two digit number such that
  the difference between 4 times the first digit
  and three times the second is seven and that when
  reversed is the number reduced by 18
• Inaudi, in two minutes, replied that there were
  no solutions.

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Jacques Inaudi (1867-1950)

• When asked to find a two digit number such that
  the difference between 4 times the first digit
  and three times the second is seven and that when
  reversed is the number reduced by 18
• Inaudi, in two minutes, replied that there were
  no solutions.

• When asked to find the number whose square and
  cube roots differ by 18, his answer of 729 was
  given in one minute.

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Jacques Inaudi (1867-1950)

• One of Inaudis remarkable traits was his
  tremendous memory for figures. In a venture to
  try and memorize a 100-figure number, Inaudi
  learned the first 36 numbers in 90 seconds, the
  first 57 numbers in 4 minutes, 75 figures in 6
  minutes and the whole number in 12 minutes.
  Within a day or two after the venture, he was
  able recall the number in its entirety.

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Jacques Inaudi (1867-1950)

• Although Inaudi did not attend any educational
  institutions nor did he reach great heights like
  George Parker Bidder, Jacques Inaudi did have a
  long and successful career as a performer
  appearing in the United States and all over
  Europe.
• In 1950, while in relative poverty, Inaudi died
  at the age of 83.
• Inaudi will always be remembered as the mild,
  modest, calm and very reserved man who, until the
  final days of his life, continued to amuse his
  neighbours with his powers.

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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?
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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?

• Like for any language, when one fails to speak
  it, the ability to recall the language may be
  that much more difficult.

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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?

• Like for any language, when one fails to speak
  it, the ability to recall the language may be
  that much more difficult.
• For those prodigies who excelled later in life,
  much can be said about their ability to prevent
  any intrusion of other interests interfere with
  their everyday lives.

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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?

• Like for any language, when one fails to speak
  it, the ability to recall the language may be
  that much more difficult.
• For those prodigies who excelled later in life,
  much can be said about their ability to prevent
  any intrusion of other interests interfere with
  their everyday lives.
• This focus allows the individual to develop their
  gift.

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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?

• Like for any language, when one fails to speak
  it, the ability to recall the language may be
  that much more difficult.
• For those prodigies who excelled later in life,
  much can be said about their ability to prevent
  any intrusion of other interests interfere with
  their everyday lives.
• This focus allows the individual to develop their
  gift.
• If the prodigy wishes to, the unlimited amount of
  time available can really allow the prodigy to
  hone in on their abilities.

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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?

• Like for any language, when one fails to speak
  it, the ability to recall the language may be
  that much more difficult.
• For those prodigies who excelled later in life,
  much can be said about their ability to prevent
  any intrusion of other interests interfere with
  their everyday lives.
• This focus allows the individual to develop their
  gift.
• If the prodigy wishes to, the unlimited amount of
  time available can really allow the prodigy to
  hone in on their abilities.
• Mental arithmetic requires
• - no instruments, or apparatus
• - no audible practice that might disturb
  members of the family
• - no information, much can be found by asking
  or absorbing
• The young individual may, at any time of the day,
  carry on with their practice and research.

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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?

• When calculating ability falls off, it may well
  be due to loss of motivation and hence failure to
  keep in practice.

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How long do these powers last?Do they stay with
the individual until their dying day or do they
merely fade as the years pass?

• When calculating ability falls off, it may well
  be due to loss of motivation and hence failure to
  keep in practice.
• For those whose gift disappeared later in life,
  they had no recollection of the methods used in
  childhood to obtain the once easy solutions to
  the once trivial questions.

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How do you account for lightning quick
calculation?

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How do you account for lightning quick
calculation?

• Gauss states that in order to make lightning
  quick calculations, you will need

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How do you account for lightning quick
calculation?

• Gauss states that in order to make lightning
  quick calculations, you will need
• 1. a powerful memory

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How do you account for lightning quick
calculation?

• Gauss states that in order to make lightning
  quick calculations, you will need
• 1. a powerful memory

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How do you account for lightning quick
calculation?

• Gauss states that in order to make lightning
  quick calculations, you will need
• 1. a powerful memory
• 2. a real ability for calculation

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How do you account for lightning quick
calculation?

• Gauss states that in order to make lightning
  quick calculations, you will need
• 1. a powerful memory
• 2. a real ability for calculation

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How do you account for lightning quick
calculation?

• Gauss states that in order to make lightning
  quick calculations, you will need
• 1. a powerful memory
• 2. a real ability for calculation
• If, for any reason, the arithmetical prodigy
  loses interest in calculation, or the opportunity
  to practice it, his power is likely to diminish
  or disappear entirely. In this respect, mental
  calculation is like piano-playing, or any other
  highly specialized activity dependent on long
  practice.

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How do you account for lightning quick
calculation?

• The more shortcutsthe better.

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How do you account for lightning quick
calculation?

• The more shortcutsthe better.
• Types of shortcuts
• 1. Arithmetical

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How do you account for lightning quick
calculation?

• The more shortcutsthe better.
• Types of shortcuts
• 1. Arithmetical
• 2. Psychological

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Why are there far fewer recorded cases of female
prodigies?
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Why are there far fewer recorded cases of female
prodigies?

• Apparent reasons for this discrepancy can be
  attributed to underreporting, lack of opportunity
  to develop the talent, and lack of encouragement
  for continued advancement.

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Why are there far fewer recorded cases of female
prodigies?

• Apparent reasons for this discrepancy can be
  attributed to underreporting, lack of opportunity
  to develop the talent, and lack encouragement for
  continued advancement.
• For many parents, the thought of taking their
  daughters across the country to make professional
  appearances was somewhat unattractive. This can
  be attributed to the fact that very few women
  gained distinction, particularly in fields
  associated with mathematics and calculation.
• most females having such talents would most
  likely have been ignored or more importantly been
  discouraged from displaying it.

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Why are there far fewer recorded cases of female
prodigies?

• Unlike the young men who would spend their young
  days with blacksmiths or tending to the family
  flock, very few girls had the opportunity to
  isolate themselves where they could then develop
  any calculating ability.
• They were not sent out on lonely vigils with
  sheep their chores were apt to be carried out in
  the presence of others.
• Too much human interaction is detrimental to the
  development of mental calculation.

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Top Five Women Prodigies/ Mathematicians in
History
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Top Five Women Prodigies/ Mathematicians in
History

• Mary Fairfax Somerville (1780-1872)
• - Scottish and British - Mathematician
• - known as the "Queen of Nineteenth Century
  Science," she fought family opposition to her
  study of math, and not only produced her own
  writings on theoretical and mathematical
  science, she produced the first geography text
  in England.

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Top Five Women Prodigies/ Mathematicians in
History

• Sophie Germain (1776-1830)
• - French - mathematician
• - She studied geometry to escape boredom during
  the French Revolution when she was confined to
  her family's home, and went on to do important
  work in mathematics, especially her work on
  Fermat's Last Theorem.

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Top Five Women Prodigies/ Mathematicians in
History

• 3. Maria Gaetana Agnesi (1718-1799)
• - Italian (Milan) - mathematician
• - Oldest of 21 children and a child prodigy who
  studied languages and math, she wrote a textbook
  to explain math to her brothers which became a
  noted textbook on mathematics. She was the first
  woman appointed a university professor of
  mathematics.

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Top Five Women Prodigies/ Mathematicians in
History

• Elena Cornaro Piscopia (1646-1684) - Italian
  (Venice) - mathematician, theologian
• - She was a child prodigy who studied many
  languages, composed music, sang and played many
  instruments, and learned philosophy, mathematics
  and theology. Her doctorate, a first, was from
  the University of Padua, where she studied
  theology. She became a lecturer there in
  mathematics.

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Top Five Women Prodigies/ Mathematicians in
History

• Hypatia of Alexandria (355 or 370415)
• - Greek - philosopher, astronomer,
  mathematician - She was the salaried head of the
  Neoplatonic School in Alexandria, Egypt, from
  the year 400. Her students were pagan and
  Christian young men from around the empire.

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How do they do that?
87
How do they do that?

• Day-Date Calculations
• One problem favoured by many calculating
  prodigies is to name the day of the week for any
  given date.
• It is necessary to memorize a special value or
  code for each month of the year, thus

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How do they do that?

• Day-Date Calculations
• One problem favoured by many calculating
  prodigies is to name the day of the week for any
  given date.
• It is necessary to memorize a special value or
  code for each month of the year, thus
• Month Value Month Value
• January 3 July 2
• February 6 August 5
• March 6 September 1
• April 2 October 3
• May 4 November 6
• June 0 December 1

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How do they do that?

• Day-Date Calculations
• One problem favoured by many calculating
  prodigies is to name the day of the week for any
  given date.
• It is necessary to memorize a special value or
  code for each month of the year, thus
• Month Value Month Value
• January 3 July 2
• February 6 August 5
• March 6 September 1
• April 2 October 3
• May 4 November 6
• June 0 December 1
• In leap years, values for January and February
  are reduced by one.

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How do they do that?

• Also, Day Values are as follows
• Day Value
• Sunday 1
• Monday 2
• Tuesday 3
• Wednesday 4
• Thursday 5
• Friday 6
• Saturday 0

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What day does October 5, 1888 fall on?

92
What day does October 5, 1888 fall on?

• 1. Take the last 2 digits of the year 88

93
What day does October 5, 1888 fall on?

• 1. Take the last 2 digits of the year 88
• 2. Add a quarter (one fourth of 88 is 22) which
  makes the total 110.

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What day does October 5, 1888 fall on?

• Month Value
• June 0
• September, December 1
• April, July 2
• January, October 3
• May 4
• August 5
• Feb, March, November 6

• 1. Take the last 2 digits of the year 88
• 2. Add a quarter (one fourth of 88 is 22) which
  makes the total 110.
• 3. Add the index for the month (October 3)
• which brings our total to 113

95
What day does October 5, 1888 fall on?

• Month Value
• June 0
• September, December 1
• April, July 2
• January, October 3
• May 4
• August 5
• Feb, March, November 6

• 1. Take the last 2 digits of the year 88
• 2. Add a quarter (one fourth of 88 is 22) which
  makes the total 110.
• 3. Add the index for the month (October 3)
• which brings our total to 113
• 4. Add the day of the month (5) and we now have
  118.

96
What day does October 5, 1888 fall on?

• Month Value
• June 0
• September, December 1
• April, July 2
• January, October 3
• May 4
• August 5
• Feb, March, November 6
• Day Value
• Sunday 1
• Monday 2
• Tuesday 3
• Wednesday 4
• Thursday 5
• Friday 6
• Saturday 0

• 1. Take the last 2 digits of the year 88
• 2. Add a quarter (one fourth of 88 is 22) which
  makes the total 110.
• 3. Add the index for the month (October 3)
• which brings our total to 113
• 4. Add the day of the month (5) and we now have
  118.
• 5. Divide this number by 7 and we get a remainder
  of 6.
• Based on the index for the day, a reminder of 6
  represents Friday.
• This calculation works for dates concerned with
• the 19th century (1801-1900).

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Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 46²?

98
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 46²?
• 1. Take the difference between 25 and 46
• 46 25 21

99
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 46²?
• 1. Take the difference between 25 and 46
• 46 25 21
• The number 21 (in hundreds) is the first 2
  numbers of the solution.

100
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 46²?
• 1. Take the difference between 25 and 46
• 46 25 21
• The number 21 (in hundreds) is the first 2
  numbers of the solution.
• 2. Take the difference between 50 and 46
• 50 46 4

101
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 46²?
• 1. Take the difference between 25 and 46
• 46 25 21
• The number 21 (in hundreds) is the first 2
  numbers of the solution.
• 2. Take the difference between 50 and 46
• 50 46 4
• Now, square that difference and we have 4²
  16.
• The number 16 gives the last 2 numbers of the
  solution.

102
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 46²?
• 1. Take the difference between 25 and 46
• 46 25 21
• The number 21 (in hundreds) is the first 2
  numbers of the solution.
• 2. Take the difference between 50 and 46
• 50 46 4
• Now, square that difference and we have 4²
  16.
• The number 16 gives the last 2 numbers of the
  solution.
• Therefore, 46² 2116 or 2100 16 2116.

103
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 29²?

104
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 29²?
• 1. 29 25 4

105
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 29²?
• 1. 29 25 4
• 2. 50 29 21
• 21² 441

106
Squaring Numbers

• For any numbers from 25 to 50
• e.g., What is 29²?
• 1. 29 25 4
• 2. 50 29 21
• 21² 441
• Therefore, 400 441 841

107
Squaring Numbers

• For any numbers from 50 to 100
• e.g., What is 88²?

108
Squaring Numbers

• For any numbers from 50 to 100
• e.g., What is 88²?
• 1. Take the difference between 88 and 50
• 88 50 38

109
Squaring Numbers

• For any numbers from 50 to 100
• e.g., What is 88²?
• 1. Take the difference between 88 and 50
• 88 50 38
• Then, doubling 38 will give us 76

110
Squaring Numbers

• For any numbers from 50 to 100
• e.g., What is 88²?
• 1. Take the difference between 88 and 50
• 88 50 38
• Then, doubling 38 will give us 76
• 2. Take the difference between 100 and 88
• 100 88 12

111
Squaring Numbers

• For any numbers from 50 to 100
• e.g., What is 88²?
• 1. Take the difference between 88 and 50
• 88 50 38
• Then, doubling 38 will give us 76
• 2. Take the difference between 100 and 88
• 100 88 12
• Now, square that difference and we have 12²
  144.

112
Squaring Numbers

• For any numbers from 50 to 100
• e.g., What is 88²?
• 1. Take the difference between 88 and 50
• 88 50 38
• Then, doubling 38 will give us 76
• 2. Take the difference between 100 and 88
• 100 88 12
• Now, square that difference and we have 12²
  144.
• Therefore, 7600 144 7744 or 88² 7744

113
Cubing Numbers

• To find the cube of any 2-digit number, it would
  be
• advantageous to memorize the cubes of the
  numbers from
• 1 to 9.
• If one wishes to find the value of 62³
• 1. Put down the cube of the first term in
  thousands.
• 6³ 216 therefore 216 000
• 2. Put down the cube of the last term
• 2³ 8
• thus, adding 216 000 and 8 will produce 216
  008.
• 3. Add to this the product of 62 and 36 (36 6
  x 2 x 3)
• 62 x 6 x 2 x 3 2232
• Therefore, 216 008
• 22 32
• 238 328
• 62³ 238 328

114
Cubing Numbers

• Find the value of 93³.

115
Cubing Numbers

• Find the value of 93³.
• 1. 9³ 729

116
Cubing Numbers

• Find the value of 93³.
• 1. 9³ 729
• 2. 3³ 27

117
Cubing Numbers

• Find the value of 93³.
• 1. 9³ 729
• 2. 3³ 27
• Therefore, 729 000 27 729 027

118
Cubing Numbers

• Find the value of 93³.
• 1. 9³ 729
• 2. 3³ 27
• Therefore, 729 000 27 729 027
• Now, 93 x 9 x 3 x 3 7533

119
Cubing Numbers

• Find the value of 93³.
• 1. 9³ 729
• 2. 3³ 27
• Therefore, 729 000 27 729 027
• Now, 93 x 9 x 3 x 3 7533
• As a result, 729 027
• 75 33
• 804 357
• Therefore, 93³ 804 357.

120
Gifted Children Speak Out
121
Gifted Children Speak Out

• What do you think being gifted means?

122
Gifted Children Speak Out

• What do you think being gifted means?
• It means you can do lots of things without help
  from grownups.
• Girl, 10
• I think smart and gifted are totally different.
  Being smart is just being able to answer
  questions and answer dates. Being gifted means
  you gave an imagination and spirit and you are
  able to think creatively.
• Girl, 10
• Gifted means being selected to attend a resource
  room because of your behaviour and your ability
  to think and learn a lot easier than others.
• Boy, 9
• I think being gifted means having a special gift
  from God, I feel that if you are gifted, you are
  on Earth to fulfill a need that other people
  cant fulfill.
• Girl, 12

123
Gifted Children Speak Out

• What is your reaction to being called gifted?

124
Gifted Children Speak Out

• What is your reaction to being called gifted?
• I dont mind being called gifted as long as Im
  not stereotyped as being perfect.
• Boy, 9
• I think the word gifted is perfect, because it
  means we have a gift to understand things
  others dont.
• Girl, 13
• I dont like being called gifted its
  embarrassing and its like bragging.
• Boy, 9
• Sometimes people think gifted means stuck up
  and they think that you are going to make fun of
  their grades because they dont make as good
  grades as you do.
• Girl, 13

125
Gifted Children Speak Out

• Are you gifted?

126
Gifted Children Speak Out

• Are you gifted?
• I do think I am smarter than most kids my age,
  but in only one way I put my brain to use and
  make it do what everyones brain can do if they
  would try to do it, or care.
• Girl, 9
• Ive never really considered myself a genius but
  yes, I think Im smart because I always seem to
  know the answer to the questions no matter what
  the questions might be.
• Boy, 13
• I really dont think I am any more gifted than
  any of my friends I just work very hard at
  everything I do and usually I do very well.
• Girl, 12
• I dont think that I am gifted because I can
  always learn something from others.
• Boy, 10