This file is part of the JOBAD demo for the AI Mashup Challenge 2009!
For the JOBAD demo, you need Firefox 3.5. You can look up the
definition of a symbol by right-clicking on it and selecting “lookup
definition” from the context menu.
Conceptequivalence
A symbol describing the equivalence relation
Definition
If one shape can become another using turns, flips and slides, then the two shapes are said to be congruent. The symbol used to denote that two shapes are congruent is
≅
.
Conceptsimilarity
A symbol describing the similarity relation
Definition
Two shapes are similar is the only difference between them is their size, and possibly the need to turn or flip one around. The symbol that is used to denote that two shapes are similar is
≈
.
Conceptproportional
A symbol describing the proportional to relation
Definition
Given two variables
x
and
y
,
y
is proportional to
x
if there is a non-zero constant
k
, such that
(
y
=
(
k
x
)
)
. The relation is often denoted by the symbol
∝
.
Concepttriangle
A constructor function that constructs a triangle from three given points.
Conceptsegment
A constructor function that constructs a segment from two given points.
Example
City
A
is
(
100
metre
)
100
from city
B
and
(
150
metre
)
150
from city
C
. What is the distance between
B
and
C
if on a map the cities are connected as shown in the figure on the left with the distances measured in centimeters.
Solution: Because the map only scales down the real dimensions we have that the triangles formed by the cities
A
,
B
and
C
and their corresponding points on the map
A'
,
B'
and
C'
are similar, i.e.
Δ
A
B
C
≈
Δ
A'
B'
C'
⇒
A
B
¯
∝
A'
B'
¯
, and
A
C
¯
∝
A'
C'
¯
as well as
B
C
¯
∝
B'
C'
¯
Using this, one can easily calculate the value of
B
C
¯
.
(
A
B
¯
A'
B'
¯
=
B
C
¯
B'
C'
¯
)
⇒
(
(
100
metre
)
4
=
x
8
)
100
4
8
⇒
(
x
=
(
200
metre
)
)
200
So the distance between the cities
B
and
C
is
(
200
metre
)
200
.
