Maps and Math

1
Maps and Math

• Historical contexts

2
Size and scale

• A quick note

3
Europe
http//www.petrarch.petersadlon.com/map.html?year
1400
Europe in 1400
4
Prince Henry the Navigator

• Few dared to venture beyond the Strait of
  Gibraltar (Pillars of Hercules)
  
• The end of the known flat Earth.
• Cape St. Vincent lies in the southwestern tip of
  Portugal and, hence, Europe.

Gibraltar and Ceuta
http//meted.ucar.edu/mesoprim/gapwinds/print.htm
5
Prince Henry the Navigator

• Prince Henry established his institute _at_ Sagres
• The capture of Ceuta by Portuguese troops
  quenched Prince Henry's passion for warfare
  
• Also launched his intellectual curiosity about
  exploration.
  
• the more he heard from prisoners, the more he was
  intrigued by this vast land

Gibraltar and Ceuta
http//www.portugalvirtual.pt/_tourism/algarve/
6
Henrys Intentions

• To establish trade relations advantageous to
  Portugal.
  
• To seek allies to help wage battles against the
  enemies of Christianity.
  
• To spread Christianity.

http//www.ucalgary.ca/applied_history/tutor/eurvo
ya/henry2.html
One night as Prince Henry of Portugal lay in bed
it was revealed to him that he would render a
great service to our Lord by the discovery of the
said Ethiopias...in these lands so much gold and
rich merchandise would be found as would maintain
the King and the people...of Portugal. Duarte
Pachece Pereira, Portuguese Explorer, 1506
http//www.pbs.org/wgbh/aia/part1/1p259.html
7
Henrys Navigation School
The beginning of the end of end of the world

• Sailors, astronomers, cartographers, and
  geographers began to arrive at Sagres to offer
  their services to Prince Henry.
  
• There were Christians, Jews, and
• Arabs--Prince Henry had discovered the Arabs'
  superior navigational skills while at Ceuta years
  before
  
• Sagres was not so much a school of navigation as
  much as it was a community of scholars, under the
  direction of Prince Henry

8
Prince Henry his alumni

• In addition to the achievements of Columbus,
  Cabot , Vespucci, Cartier, da Gama and others in
  the discovery of the Americas
  
• Bartolomeu Dias (1457-1500) had circumnavigated
  the Cape of Good Hope Vasco da Gama had been the
  first explorer to reach India by sea (1498)
  
• Francisco Magellan's almost-complete global
  circumnavigation
  
• In the mid-16th century Portuguese merchants and
  Jesuit missionaries had made contact with Japan
  
• About 50 years later the Dutch had established
  their first trading posts in South-East Asia.

9
Maps from a long time ago
Mesopotamian City Plan, Nippur 1500 BC

• Maps were made across many civilizations
• Some were attempts to draw to scale
• Some based not on reality but on faith

Babylonian clay tablet world map, 600 B.C.
10
Flat or Spherical?

• A sense of Earths shape came from observing the
  surroundings . including the sky
  
• The link between geometry and astronomy
• from the apparent movement of the stars
• The ships gradually vanishing, hull first
• The shape of the shadow during the eclipse
• (which itself needed a prior understanding that
  eclipses were not caused by demons)

11
Alexandria

• Alexander founded the city as a regional capital
• Ptolemy, a Macedonian, was the ruler of Egypt
  after Alexanders death
  
• The Ptolemy dynasty ended with Cleopatra
• Ptolemy XIII was her brother and husband
  (Ptolemaic tradition institutionalized incest!)
  
• A great library founded
• Eratosthenes made the chief librarian by Ptolemy
  III

12
Earths circumference

• Eratosthenes starting points
• 1. once a year (on the day of the Summer
  solstice), the bottom of a well situated at Syene
  (Aswan) in Upper Egypt was illuminated by the
  Sun
• 2. However, at Alexandria, this never happened
  obelisks always cast a shadow
  
• 3. He believed that Earth was a sphere
• 4. He assumed that Alexandria and Syene were on
  the same meridian
  
• 5. He knew (or better, he assumed) that the
  distance between the two cities was 5,000 stadia
  (as caravans covered the distance in 50 days at a
  rate of 100 stadia a day)
• 6. He postulated that sunrays reached Earth as
  parallel beams

13
Eratosthenes Calculations

• On solstice day, he decided to measure the length
  of the meridian shadow cast by a gnomon at
  Alexandria.
  
• He found a value of 1/50th of a circumference
  (i.e. 7o 12')
  
• The circumference was, therefore, 505000250,000
  stadia
  
• about 46,000 kilometers

14
The other Ptolemy

• Unrelated to the dynasty this is the Ptolemy
  referred to in the LA Times article
  
• Some of the ideas from him
• Dividing a degree of a circle into minutes and
  seconds
  
• Drawing maps to scale, and hence different scales
  for different maps
  
• Latitude and longitude
• Map projections (equal areas)

The Almagest, written about A.D. 150
15
No reason

• Unlike the systematic (scientific) approach of
  Eratosthenes
  
• Cosmasa sixth century convert to Christianity
• Based his geography on the writings of Saint
  Paul
  
• The world as a vast tabernacle a tent with a
  rectangular base, twice as long as it was broad,
  and with an arched roof supported by for pillars
  
• the earth was flat and twice as long, from east
  to west, as it was broad

16
Patron Saint of Computers

• Saint Isidore (560-636 AD)
• Notice how the map is oriented?
• Tanais refers to the river Don (fourth longest in
  Europe)

And Quiet Flows the Don
http//www.catholic-forum.com/saints/sainti04.htm
17
Road map to the world

• Marcus Agrippas surveys of iter
• Roads and landmarks shown
• not to scale, nor to true direction
• Practical maps, as opposed to
• the mappaemundi, which were artistic
• Ptolemys, which attempted scientific precision

18
Results of globalization

• As Europe started crawling out the Dark Ages,
  interactions grew with Arabs, Chinese, and
  Indians
  
• who had continued on with scientific mapmaking
• Main source of information now were the mariners
  and the pilots notes
  
• Portolan Charts

19
Portolan Maps

• Orientation towards north
• because of the use of the magnetic lodestone
• Chinese use of lodestone as a compass
• Portolan charts developed a network of rhumb
  lines
  
• constant course
• How is this related to the Mercator map?

20
Oh Henry !

• Step 1 was to explore beyond Cape Bojador
• The disappearance of numerous European attempts
  to round the Cape led some to suggest the
  presence of sea monsters
  
• In 1434 Gil Eanes achieved the feat
• Step 2, to sail around Africa
• In 1488 Bartholomew Diaz accomplished this
• Ended Ptolemys idea that Africa connected with
  Terra Incognita