these are a few of my favorite things l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
These are a few of my favorite things..... PowerPoint Presentation
Download Presentation
These are a few of my favorite things.....

Loading in 2 Seconds...

play fullscreen
1 / 27

These are a few of my favorite things..... - PowerPoint PPT Presentation


  • 343 Views
  • Uploaded on

These are a few of my favorite things. Using History to “Spice” up a Math Class Shawnee McMurran mcmurran@math.csusb.edu. Algebra: Completing the Square. Abu Ja'far Muhammad ibn Musa Al-Khwarizmi Born: about 780 in Baghdad (now in Iraq) Died: about 850. Al-jabr .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

These are a few of my favorite things.....


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
these are a few of my favorite things

These are a few of my favorite things.....

Using History to “Spice” up a Math Class

Shawnee McMurran

mcmurran@math.csusb.edu

algebra completing the square
Algebra:Completing the Square
  • Abu Ja'far Muhammad ibn Musa Al-Khwarizmi
    • Born: about 780 in Baghdad (now in Iraq)
    • Died: about 850
al jabr
Al-jabr
  • The Arabic word al-jabr is the source of our word algebra.
  • In Arabic al-jabr means “restoring”.
slide4

x

10

x

slide5

x

10

x

slide6

x

5

x

5

slide7

x

5

x

5

from mah v ra 9 th century india
From Mahāvīra (9th century India)
  • One night, in a month of the spring season, a certain young lady was lovingly happy along with her husband on the floor of a big mansion, white like the moon, and situated in a pleasure garden with trees bent down with the load of the bunches of flowers and fruits, and resonant with the sweet sound of parrots, cuckoos, and bees which were all intoxicated with the honey obtained from the flowers therein.
slide10
Then on a love quarrel arising between the husband and the wife, that lady’s necklace made up of pearls became sundered and fell on the floor. One-third of that necklace of pearls reached the maid-servant there; one-sixth fell on the bed; then one-half of what remained (and one-half of what remained thereafter and again one-half of what remained thereafter and so on, counting six times in all) fell all of them everywhere; and there were found to remain (unscattered) 1161 pearls.
  • Give out the measure of pearls in that necklace.
word problems it s a tradition
Word Problems:It’s a tradition
  • Bhāskara (7th century)
    • The eighth part of a troop of monkeys, squared, was skipping in a grove and delighted with their sport. Twelve remaining monkeys were seen on the hill, amused with chattering to each other. How many were there in all?
circles on the nile
Circles on the Nile
  • Cut a piece of string to be the diameter of your circle.
  • Mark a starting point on your circle.
  • Carefully lay your diameter string in the valley of your circle. Mark your new start at the end.
  • Repeat until you reach the original “start”.
  • How many diameters fit in your circle?
  • Answer: 3 and a little more (i.e. “”)
  • Using your string as a radius, draw your circle in the sands of the Nile.
a basket for pi
A Basket for Pi
  • Calculating Pi via the surface area of a “basket” (hemisphere) that is 4½ units in diameter
  • Answer: 32
  • Method: d(8/9)(8/9)d
babylonian problem sets
Babylonian Problem Sets
  • Formula for the area of a circle on a Babylonian Tablet (c.1700 BCE)
    • A=C2/12 or A=5C2 since 5 is the reciprocal of 12.
leonhard euler 1707 1783
Leonhard Euler (1707-1783)
  • 886 papers and books! (fills about 90 volumes)
  • and 13 children!
guillaume de l h pital 1661 1704
Guillaume De l'Hôpital1661-1704
  • Analyse des infiniment petits pour l'intelligence des lignes courbes (1692) was the first text-book to be written on the differential calculus
guillaume de l h pital 1661 170419
Guillaume De l'Hôpital1661-1704
  • Analyse des infiniment petits pour l'intelligence des lignes courbes (1692) was the first text-book to be written on the differential calculus
  • L'Hôpital’s Example for his rule:
  • L'Hôpital’s Rule is really Johann Bernoulli’s rule. (Unfortunately Bernoulli failed to read the fine print.)
william sealey gosset 1876 1937
William Sealey Gosset1876-1937
  • The “Student” of the t distribution
    • Gosset was a Guinness Brewery employee who needed a distribution that could be used with small samples. The brewery did not allow the publication of research results, hence the pseudonym Student.
derivatives second derivatives and recent history22
Derivatives, Second Derivatives and Recent History
  • Look at the CPI for the last 50 years – some sample questions
    • Does the data supply a possible reason for Jimmy Carter’s failure to win a second U.S. presidential term?
    • Does the data supply a possible reason for the success of George Bush, Sr. in winning the U.S. presidency?
    • Does the data supply a possible reason for the results of the latest presidential election? Explain
max or min
Max or Min?
  • How should the aircraft be proportioned to maximize range?
    • The derivative of range

with respect to volume

is zero when the volume

is almost all in the wing.

  • Oops – the second derivative is positive under these circumstances!
math victorian style
Math Victorian Style
  • Down to our own time many persons have believed that an educated mother would be “in danger of deserting her infant for a quadratic equation.”
    • (Arthur Gilman quoting Sydney Smith – 1888)
philippa fawcett
Philippa Fawcett
  • Took the Cambridge Tripos exam in 1890
  • The exam was 36 hours long spread over 6 days (140 problems)
  • She beat the senior wrangler by 400 pts, (13 percentage points)
some of those exam questions
Some of those exam questions
  • Show that the sum of the products three together of the first n odd numbers is:
  • Show that the equation

has at most three real roots.

  • Find the chance of throwing 8 at least once in n throws of a dice.
slide27
Hail the triumph of the corset

Hail the fair Philippa Fawcett

Victress in the fray

Crown her queen of hydrostatics

And the other mathematics

Wreathe her brow in bay.

If you entertain objection

To such things as conic sections

Put them ought of sight

Rather sing of the essential

Beauty of The differential

Calculus tonight.

Worthy of our approbation

She who works out an equation

By whatever ruse

Brighter than the rose of Sharon

Are the beauties of the square on

The hypotenuse.

Curve and angle let her con and

Parallelopipedon and

Parallelogram

Few can equal, none can beat her

At eliminating theta

By the river Cam.

May she increase in knowledge daily

Till the great professor Cayley

Owns himself surpassed

Till the great professor Salmon

Votes his own achievements gammon

And admires aghast.