playingwithpatternsplayingwithpatterns andrew derer mathscience innovation center richmond, virginia
TRANSCRIPT
Using Student Responders
To respond to a question:
• Wait for polling to be open.
• Select your response while aiming at the receiver.
Aim this…
…at this
From the list below, which is your favorite class?
Mat
h Cla
ss
Sci
ence
Cla
ss
Soci
al S
tudi
es C
lass
Lan
guage
Arts C
lass
Any
clas
s w
ith m
ath in
it
11% 11%
0%0%
79%1. Math Class
2. Science Class
3. Social Studies Class
4. Language Arts Class
5. Any class with math in it
What is encryption?
Mix
ing u
p num
bers
or...
Mak
ing
a pat
tern
whic
...
A s
pecia
l sys
tem
use
...
A n
ew c
omput
er ru
n...
All
of the
above
.
11%
26%
47%
0%
16%
1. Mixing up numbers or letters in no specific order.
2. Making a pattern which is impossible to decode without the key.
3. A special system used by spies to get into other countries.
4. A new computer running on the Intel Pentium VI chip.
5. All of the above.
What is a cryptex?What is a cryptex?
• A cryptex is a device credited to Leonardo DaVinci which can hold a scroll or secret note.
• It cannot be opened without the correct code.
• The one in the picture below has 5 dials and 26 letters per dial.
• This means there are approximately 11,800,000 combinations.
Encryption is…
• A defined pattern which allows users to make information useless unless decoded properly.
• A method of securing information for transport either physically or electronically.
• A defined topic in mathematics which has helped make internet commerce possible.
Finding the Code
• Your task today is to unlock the code and retrieve the prize.
• You will work in groups, but open the cryptex as a class.
• Each pattern will reveal another piece of the puzzle.
• Good Luck!
• This slide will self destruct in 10 seconds.
con
Can this sequence…
, , , , help us figure out this sequence?
2, 5, 9, 14, _____20
Can you find the nection
What is the link?
The
number
s te
ll ho
...
The
shap
e re
prese
nt...
The
number
is a
mul
ti...
Som
ethin
g els
e.
6%
29%
65%
0%
1. The numbers tell how much area the shape has.
2. The shape represents how many letters are in the number.
3. The number is a multiple or factor of the number of sides of the shape.
4. Something else.
Challenge #2: Geometry
• I can make a square with one square.• I can find the perimeter of this square.• I can also find the area.• But what happens to area and
perimeter if I add:– 1 unit to the length and – 2 units to the width?
• What if I did the same thing to this newer, larger rectangle?
• See if you can find a pattern…
The number of branches in the next row is:
0% 10%0%0%0%10%
10%
70%
12 13 14 15 16 17 18 None of the above
1. 12
2. 13
3. 14
4. 15
5. 16
6. 17
7. 18
8. None of the above
http://www.mcs.surrey.ac.uk/Personal/
R.Knott/Fibonacci/fibnat.html
Fibonacci
• Where else can we find Fibonacci numbers?
• See if you can locate Fibonacci patterns with the objects given…
The 4th is a fun one!
1 1 2 1 3 2 4 1 5 3 6 2 7 4 8 1 9 5 10 3
Can you find the next 3 numbers in the sequence.
Hmm, there’s something unique about this pattern.
Check this out!
1 1 2 1 3 2 4 1 5 3 6 2 7 4 8 1 9 5 10 3
1 1 2 1 3 2 4 1 5 3
Eliminate every number the first time it occurs and the result is…
It’s the same pattern! Whoa!
Fractal Pattern
• A pattern within a pattern within a pattern
• Here are some pictures of patterns within patterns
Our fifth challenge
• Look at the following sequence.(it uses 1’s and 2’s only).
• Can you find the next 5 numbers?
1 2 2 1 1 2 1 2 2 1 2 …
I’ll let you look at it for a while before I give you a hint
Hint: Check out the length of repetitions of numbers…
Kolakoski Sequence
1, 2, 2, 1, 1, 2, 1, 2, 2, How many numbers should the next group have?
What should the next group of numbers be?
2 questions to answer:
Kolakoski Sequence
• Some questions without answers:– Is there a formula for the nth term?– If a string (e.g. 21221) occurs in the sequence
will it occur again?– Why are hotdogs sold in packs of 10 and
buns in packs of 8?