Heron

1
Herons Formula

• Another Area formula

2
Who is Heron?

• Heron of Alexandria (also called Hero) was a
  Geometer of Egypt. There is some confusion as to
  the date he lived, but generally it appears that
  he was born in approximately 10 AD and died in 75
  AD. (Believe it or not, his name was pretty
  common, so determining lifetime of the Heron that
  we are thinking of is tough)
• He was most likely a teacher at the Museum in
  Alexandria. Notes attributed to him appear to be
  lecture notes on Physics, Mathematics, Pneumatics
  and mechanics.
• He proved Heron's Formula in Book 1 of the
  Metrica, a work that outlines methods of
  measurement.

3
Interesting to note

• Although Heron has his name on the formula, our
  book (and other resources) suggest that
  Archimedes may have actually developed Herons
  Formula, not Heron.
• Just goes to show you that just because a name is
  on it doesnt necessarily mean that person
  discovered it.
• For instance, it is known that the Chinese had
  known about Pascals Triangle for 300 years
  before Pascals time. (see pg 494 in our book)

4
What is Herons Formula?

• Weve been using the formula
• to find the area of non right triangles.
• This formula is valuable because it can be used
  with SSS triangles.
• What does that mean?
• We dont
  need an angle!!

5
Where does it come from?

• The next slide takes through the step by step of
  the derivation of Herons formula.
• You do not need to memorize it just understand
  it.

6
SSS Triangles (need to get rid of angles)
7
(No Transcript)
8
(No Transcript)
9
Examples

• Given ?ABC with a 3, b 4 and c 5, find the
  area using Herons Formula.
• 2. If ?ABC has sides 3, 4 and 5, what kind of
  triangle is it? Find the area using another
  formula for area.
• Given ?ABC with a 4, b 4 and c 6, find the
  area using Herons formula .
• Use your calculator to determine the area of the
  triangle in problem 3. Make sure that your
  answer from 3 is the same as the answer you get
  with the calculator.

10
Resources
http//www-groups.dcs.st-and.ac.uk/history/Mathem
aticians/Heron.html
Sobel, Max, Lerner, Norbert, (1995) Precalculus
mathematics 5th Edition, Englewood Cliffs, NJ,
Prentice Hall, Inc.