Self-paced
P1
Fractal geometry is a mathematical theory devoted to the study of complex shapes called fractals. ████████ ██ █████ ██████████ ██ ████████ ███ ███ ████ ████████████ ████████ ████████ ███████ ███ ████████ ██ ████████████████ ███ ███████████ ██ █████████ ███████ ██ ████████ ██ █████████████ ███████ ██████ ██ ████ ████ █████ ████ ██████████ █████ █████████ ████ ███ ██████ ██ █ ██████ ███
Spotlight ·
Fractal geometry
No exact definition of fractals, but they show self-similarity: small details in shape look like the shape as a whole.
Example ·
Koch curve
The Koch curve is an example of a fractal. (Details of what the Koch curve looks like. No need to memorize this. Will come back if asked about it.)
P2
███████████████ ██ █████ ████ ███ ████████████ ███████ ██ ████████ ████████ ██ ████ █████ ███ ████ ███ ██ ███ ████████ ███████ ███ ████████ █████ ███ █████ ███ ███████ ████ ███ █████ ██ ███████ ███
More on the Koch curve ·
Can be created by computer
Interesting point about fractal geometry ·
Simple processes can create complex patterns
This is one of the major reasons people are into fractal geometry.
P3
█ █████████ ██████ ███ ██████ ██████████ ██ ███████ ████████ █████ ███████ ███████████ ██████████████████ ██████ ██ █████████
Enthusiasts ·
Believe fractal geometry will rival importance of calculus
Also believe it will allow mathematicians to effectively describe natural forms (such as a cloud).
Skeptics ·
Fractal geometry will have lasting ro in math only if it can support theorems and proofs
Passage Style
Critique or debate
Spotlight
24.
Which one of the following ████ ███ ██████ ███████ ██ █ ██████████████ ██ ███████ █████████
a
It is potentially ████ ████ █████████ ████ █████████
Some people think it might “
b
Its role in ███████████ ███████████ ████ ██████ ██ █████████ ██████ ███████
The author doesn’t indicate that fractal geometry’s role will expand as computers become faster. Computer speed isn’t mentioned.
c
It is the ███████████████ █████ ██ ████████████
“Fastest” is not supported. The author doesn’t say it’s the “fastest-growing” field of math.
d
It encourages the ███ ██ ████████ ████████ ██ █████ ████████████ █████████
The author never suggests fractal geometry encourages people to use computer to prove theorems. Some skeptics think fractal geometry needs to prove theorems before it will become long-lasting. This doesn’t imply the author thinks fractal geometry “encourages” the use of computers for proving theorems.
e
It enables geometers ██ ████████ ███████ █████ █████ ██████ ██████████