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Who are we?
1
Lewis:
Maths Teacher
(EF Academy)
Emma:
Maths Teacher
(EF Academy)
Alonso:
PhD Student in
Engineering
Mathematics at
University of
Bristol.
Which country do you think has the longest coastline?
Does Fiji have a longer coast line than Russia?
Maybe….
Measuring Devon’s Coastline
Measuring Devon’s Coastline
Measuring Devon’s Coastline
Measuring Devon’s Coastline
So about 3.5
Measuring Devon’s Coastline
Instructions are on the
sheet!
So about 3.5
What did you find?...
As the length of the stick decreases,
the coastline length increases.
Let’s look into this a bit further.
The Koch Snowflake (Fractal)
The Koch Snowflake
1
54
32
6 ,7,8,…
Repeating pattern
What is the perimeter of the Koch snowflake?
The Koch Snowflake (Perimeter)
1 unit
1
The Koch Snowflake (Perimeter)
1/3 unit 1/3 unit
1/3 unit 1/3 unit
2
The Koch Snowflake (Perimeter)
Instructions are on the
sheet!
3 units 16
3units4 units
64
9
units
256
27
units
1024
81
units
1 32
54 6
The Koch Snowflake (Perimeter)
×𝟒
𝟑×𝟒
𝟑×𝟒
𝟑
×𝟒
𝟑
×𝟒
𝟑×𝟒
𝟑×⋯
×𝟒
𝟑
7, 8 , …
4
3= 1.33333…
1 d.p1) 3 2) 43) 5.34) 7.15) 9.56) 12.6
1 d.p1) 3 2) 43) 5.34) 7.15) 9.56) 12.6
1 d.p
100) 𝟕. 𝟎 × 𝟏𝟎𝟏𝟐
1000) 𝟔. 𝟓 × 𝟏𝟎𝟏𝟐𝟒
Koch snowflake perimeter:
Infinite!
The Koch Snowflake (Area)
The Koch Snowflake
Finite Area
Infinite Perimeter…
Does Fiji have a longer coast line than Russia?
Depends on the length of measuring stick you use!
Break…. (15mins)
Cryptography workshop
Can you crack the codes?
27
What is cryptography?
Is it important?
Why?
Cryptography is the art of
writing and solving codes.
29
There are lots of
ways to encrypt text
We can use a
different alphabet
One more example
could look like this
Letters have been
shifted to the right
Uifsf bsf
mput pg xbzt
up fodszqu
ufyu
We can
use a
different
alphabet
Using the wingdings
font
UIFSFBSFMPUT
PGXBZTUPFODS
ZQUUFYU
AES-256, used in
53 61 6c 74 65 64 5f 5f b7
e0 12 e5 7e 07 64 15 f9 c5
d0 86 12 b0 be 81 9d 60 fe
92 25 82 37 e7 c5 b6 76 98
ef e3 6b 9f 64 9f 54 e7 68
c4 4f 19 4f c5 ee cc ad 54
4c c1 13 b4 1e d7 5a 0c 39
08
There are
lots of ways
to encrypt
text
The challenge:
30
• Work in your groups to figure out who wrote your
piece of text.
• Ask one of us for the next task.
• Crack the code to try and answer this question:
Not sure what to do? Please ask for help!
How many pairs of prime numbers exist with a
difference of 2 between them? For example 5 and 7.
- - - - - - - - - -
31
If you’ve cracked the code:
How could you crack a Caeser cypher
without guessing?
What is the problem with having a
code with a secret key?
UIFSFBSFMPUT
PGXBZTUPFODS
ZQUUFYU
Thereareloto
fwaystoencry
pttext
32
How many pairs of prime numbers exist with a
difference of 2 between them? For example 5 and 7.
- - - - - - - - - -
The challenge:
33
EKOSONNNWO
Unscramble the letters below to make a sentence
34
The challenge:
N O
How many pairs of prime numbers exist with a
difference of 2 between them? For example 5 and 7.
O N E K N O W S
35
Rank Prime Number Discovered Digits
1 277232917 – 1 26/12/2017 23,249,425
2 274207281 – 1 07/01/2016 22,338,618
3 257885161 – 1 25/01/2015 17,425,170
How can we find the next largest prime
number without a computer?
(For example by using an equation or
rule)
N O O N E K N O W Shttps://en.wikipedia.org/wiki/Largest_known_prime_number
36
Prime numbers are used in encryption to
send secret messages.
It works on the basis of finding prime
factors.
37
Take two prime numbers...
7 13
And multiply them together
The result is...
= 91x
38
But what if we asked:
91
What two prime numbers make
when multiplied together?
How long would it take you to find
7 and 13?
39
Changing the number
119
What two prime numbers make
when multiplied together?
7 and 17
40
Harder numbers!
234649
What two prime numbers make
when multiplied together?
461 and 509
41
An easier question
263467
What two prime numbers make
when multiplied together?
487 and ?
42
An easier question
263467
What two prime numbers make
when multiplied together?
487 and 541
43
It is this property of prime numbers
that is used to send messages secretly!
It takes LONGER and LONGER to find the
prime factors if the numbers get
LARGER and LARGER.
Lets see how it works for real!
44
“Spies” and “Hackers” game.
You will need
a calculator
48
“Spies” and “Hackers” game.Adalyn 397
Aiden 467
Alexander 389Amelia 307
Aria 479
Aubrey 509
Ava 293
Benjamin 409
Caden 443
Caleb 263
Madison 499
Mason 349Mia 241
Michael 461
Noah 503
Oliver 233Olivia 281
Riley 359
Sophia 353
51
“Spies” and “Hackers” game.
What if you
all had 4
digit prime
numbers?
52
“Spies” and “Hackers” game.
What if you only
knew your own
prime number?
53
“Spies” and “Hackers” game.
Prime numbers
are at the heart
of cryptography!
54
Thank you!
Also thanks
to these
guys at..
Sam: swarm
robotics.
Paisley:
tumour
growth.
Jake:
supercomputers.
Sam: learning
from data.
youtube.com/computerphile
numberphile.com
youtube.com/TomScottGo
YouTube Channels to check out
Thank you!
Please fill
out our
questionnaire
to make this
session even
better!
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