FRITS STAAL
GREEK AND VEDIC GEOMETRY
I. RITUAL GEOMETRY
It has been somewhat of an embarrassment to Euro-American classicists
that the earliest Pre-Socratics, the Milesian or Ionian natural philosophers with which Greek philosophy began, were inhabitants
Which Garage is Better?
TEACHER NOTES
About the Lesson
In this activity, students are to find the solution to a system of
linear equations using technology. They are presented with a
problem on parking lot fees. As a result, students will:
Graph a linear
Old MacDonalds Pigpen
TEACHER NOTES
About the Lesson
In this activity, students explore numerically, graphically,
algebraically, and verbally the mathematics involved in
maximizing the area of a rectangle with a fixed perimeter. As a
result, students will
The Pythagorean Theorem
TEACHER NOTES
About the Lesson
In this activity, students will construct figures that prove the
Pythagorean Theorem in two different ways. As a result, students
will:
Construct and measure the side lengths of several right triangl
Old MacDonalds Pigpen
Name
Student Activity
Class
Old MacDonald has 40 meters of fencing to make a rectangular pen for his pigs. If he wants to give the
little pigs as much room as possible, what dimensions should he make the pen? To figure this out, he
d
The Pythagorean Theorem
Name
Student Activity
Class
Problem 1 Squares on Sides Proof
1.
Why is the constructed quadrilateral a square?
2. Record three sets of area measurements you made by dragging points A, B, and/or C.
Square on BC
3.
Square on AC
Sum o
Which Garage is Better?
Name
Student Activity
Class
The cost schedules for two different parking garages are below. The maximum stay is 24 hours.
Blue Street Garage
Length of time in the garage
1 hour or less
Cost
A flat fee of $10.
$10 for the first hour
Accuracy, Precision and Uncertainty
How tall are you? How old are you?
When you answered these everyday
questions, you probably did it in
round numbers such as "five foot, six
inches" or "nineteen years, three
months." But how true are these
answers? Are
Eukaryotic (true nucleus) cells
contain organelles
Organelles:
Are membrane bound
Are sub-cellular structures
Perform a specific function for
the cell
Types of Eukaryotic Cells
Animal Cells
Plant Cells
Protist Cells
Fungi Cells
Major Parts of the Eukaryot
Phylum: Chordata
Organisms with a dorsal
nerve cord
Bilateral symmetrical
Can be vertebrates or
invertebrates
Invertebrate chordates - tunicates
and lancelets
Small chrodates that
live in marine sand
Have chordate
features and
segmental muscles
which
Phylum: Cnidarians
Phylum: Cnidarian
Examples: hydras,
jellies, sea anemones
and corals
All have radial symmetry
They are carnivores and
use their tentacles to
capture small animals
and protists and push the
prey into their mouths
Have stinger cells o
Phylum: Echinodermata
Phylum: Echinodermata
Examples: sea stars, sand
dollars, sea urchins
Most are radially symmetrical
Can have hard spines or
plates embedded under the
skin which are actually part
of the hard internal skeleton
(endoskeleton)
Can re
Phylum: Molluska
Phylum: Molluska
Snails, slugs, oysters,
clams, octopuses and
squids
Most have a soft body
protected by a hard
shell
Have a true body
cavity and a
circulatory system
Bilateral symmetry
Phylum Porifera: Sponges
Sponges have a simple porous body
Simplest of all animals, have no nerves or muscles, they
dont really have tissues because the cells are relatively
unspecialized
Suspension feeders feed by collecting bacteria from
water that s
Phylum: Annelida
Phylum: Annelida
Annelids are segmented
worms with bilateral
symmetry
The subdivision of the body
along its length into a series
of repeated parts allows
greater flexibility and mobility
Examples:
Earthworms till the soil and
improve