MOTION MEASUREMENT
AND CONTINUITY

Form a

Euclidean vector space

According to
Mathematicians

Called GALILEAN
Velocity

Does not need

Space

time

Measurement
to be defined

Can

Be distinguished

Change gradually

Point somewhere

Be compared

Be added

Have defined angles

Distances is

r = R2 /r.

Flatness

Is defined with
the help of

Bodies

Radiation

is deduced by
comparing motion

Sequences of
all instants

The smallest part
is called

Events

Instants of
time

can have vanishing duration

are equal for all observers

Can be distinguished

can be put in order

define duration

do not end

don´t habour surprises

Clocks

moving system whose
position can be read

types

Stopwatches

Sundials

Lunar clocks

Seasonal
clocks

Distinguish positions

with our senses

Properties
Galilean space

Can be
distinguished

Can be lined up
if on one line

Can form
shapes

Define
distances

Define
angles

Can beat
any limit

vanishing
distances

Coordinates (x,y,z)

they specify the
location

Length

Straight lines

Is used to defined

Volume

Values be
Additive and rigid

rectangular polyhedron a, b, c as V = abc.

a general polyhedron cannot
be cut into a cube by straight cuts

discovered by
Max Dehn

Area

Values be
Additive and rigid

Itegration
method

where can define area for nicely curved shapes
as the limit of the sum of infinitely many polygons.

a and b as A = ab