MOTION MEASUREMENT
AND CONTINUITY
SIZE
Length
Straight lines
Is used to defined
Area
a and b as A = ab
Itegration
method
where can define area for nicely curved shapes
as the limit of the sum of infinitely many polygons.
Volume
rectangular polyhedron a, b, c as V = abc.
a general polyhedron cannot
be cut into a cube by straight cuts
discovered by
Max Dehn
Values be
Additive and rigid
SPACE
Properties
Galilean space
vanishing
distances
Can beat
any limit
Define
angles
Define
distances
Can form
shapes
Can be lined up
if on one line
Can be
distinguished
Distinguish positions
with our senses
TIME
Clocks
moving system whose
position can be read
types
Seasonal
clocks
Lunar clocks
Sundials
Stopwatches
Instants of
time
don´t habour surprises
do not end
define duration
can be put in order
Can be distinguished
are equal for all observers
can have vanishing duration
Sequences of
all instants
The smallest part
is called
Events
is deduced by
comparing motion
STRAIGHT
Is defined with
the help of
Radiation
Bodies
Flatness
HOLLOW EARTH
r = R2 /r.
Distances is
VELOCITY
Can
Have defined angles
Be added
Be compared
Point somewhere
Change gradually
Be distinguished
Does not need
time
Measurement
to be defined
Space
Form a
Euclidean vector space
Called GALILEAN
Velocity
According to
Mathematicians
