Substitution Cipher (Hiya Ganju)

The main problem with the encryption method is that it can be
easily deciphered using frequency analysis. Frequency analysis is effective to
break down the encryption method because all the letters of the alphabet are in
order, meaning that when one letter code has been cracked, all the others are
also easy to crack, further leading to its inefficiency.

In order to prevent this from happening, the use of symbols,
different languages and various methods of encryption should be applied. This
will result in the reduction of deciphering the encryption method using the
frequency method or at least, make it more difficult.

#exploremaths

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Substitution Cipher (by Sandeep Darapuneni)

#exploremaths

The substitution
cipher has one glaring problem to it; that frequency analysis of the symbols used
can be compared with the usage of the English letters to find out what a
message means. But this method is only effective when used on long messages. It
is kind of like reliability in science. If someone could send multiple short
messages, it would mean that it could be harder to break.

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The Substitution Cipher (Eric Sun)

A major flaw in the alphabet shifting method is that it
could be easily solved using frequency analysis. A way that you could alter the
code: Substitute all the letters for something else like numbers or Greek
letters and mirror image the message.

#exploremaths

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Substitution Cipher (Josh Luong)

1. What is one problem with the substitution cipher?

Shown in the video, it is noticeable that this encryption
method was flawed because of how it was solvable using the frequency analysis.
Frequency analysis is when you find a common letter used in the English
alphabet such as ‘e’ and by finding another letter that is just as common and
using that code scheme to work out the whole message.

2.What is one way to overcome this problem?

A way that we could solve this problem is by not only
encrypting the message 1 way but multiple. For example we could make the
message translated into several other languages that use the same shapes as the
letters in the English alphabet such as French or German then  that way the message will have another
process that it must be solved before readable.

 #exploremaths

Alphabet Shifting Cipher (Alex Ho)

The alphabet shifting cipher, although useful for mixing up
the letters, has its own flaw. Frequency analysis. The use of finding common
letters forming a small word can easily destroy the point of a cipher. Finding
just a couple of letters, and matching them up will lead to the match up of the
other missing letters without the person ever having to work them out.

To make this method better would be using more fancy words
and synonyms of common words, to allude the cracker. Another would be to use a
completely different cipher with different symbols and keys.

#exploremaths

Cryptography (by Erik Willison)

#exploremaths
The major flaw in the alphabet shifting method was that it can easily be deciphered using frequency analysis
A way that you could alter this code in order to make it better, you could not use words with common letters in them although this may be a tad impractical. you could also use multiple symbols to represent the most common letters so that it would appear that you are writing with more than 26 letters. Other than that my other suggestions are to make the code you’re using completely different because quite frankly it is banal and rudimentary.

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AT5 – Stage 0 [Josh Luong, Adam Tan, David Yoo]

Group: Joshua Luong, Adam Tan, David Yoo

Video Concept: Documentary (David Attenborough/Man vs Wild style)

As a group, we brainstormed various methods of how we wished to present our concepts and we agreed on creating an informative, documentary-styled clip. Hopefully, the final result will project a creative and humorous exploration of various concepts of maths that are found in our daily lives. 

Ideas so far:

– Mathematical concepts used in real life (eg. cooking/construction/anything with units)

– Mathematics applied in everyday physics (eg. sports)

– Mathematically based games

– Multiple clips edited together

– Charismatic voices (otherwise it wouldn’t be a good documentary, of course)

– Filming both in and out of school

– Golden rectangles … golden rectangles everywhere

– Hollywood level acting

– Hollywood level editing

– Getting clips from different environments

#exploremaths

Discovery or invention? (by Michelle So)

Mathematics is the language mankind use to communicate mathematical ideas. It has been a widely debated topic whether mathematics was discovered or an invention. My first thought when I was asked this question was mathematics was discovered as the mathematics discovered in nature such as the golden ratio or tessellations were not invented by mankind; instead they were already there long before the existence of mankind. Even if humans didn’t discover these mathematical ideas, they would have still existed. Humans simpily identified the concept behind these ideas and gave it a name.

However, as it thought more about this question, I realize there are aspects of mathematics which were created by humans: algebra, number systems. If humans disappeared, these mathematical aspects would also follow. As a result of this, I came to a conclusion that mathematics is both discovered and invented.

#exploremaths

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Number Systems (by Michelle So)

Hexadecimal

What is the purpose of this number system, and what are its distinctive features?

Hexadecimal is a number system with the base of 16. It is used as a short hand for binary numbers, allowing binary system to be expressed in fewer characters. The distinctive features of hexadecimal system are that it uses sixteen symbols. In most cases, the values zero to nine is represented by the symbols 0-9 and the values ten to fifteen is represented by the symbols A,B,C,D,E,F.

Explain where and how this number system is used today.

The hexadecimal number system is now broadly used by computer systems designers and programmers. In order to represent these hexadecimal constants in computing languages, different notations are used. In addition to this, this number system is also used in tradition Chinese units for weight.

What are the advantages and disadvantages of this number system?

The advantage of this number system is that it is very easy to convert between binary number and hexadecimal numbers and it allows binary numbers to be expressed in fewer symbols. The disadvantage of this number system is since it is not a base of 10 system, it causes errors to be made as it is a system with a base of 16.

 

Egyptian Number System

What is the purpose of this number system, and what are its distinctive features?

The Egyptian Number System was used for a wide variety of occasions, theses included, measuring time, straight lines, the level of the Nile floodings, calculating areas of land, counting money, working out taxes and cooking. In this system, it uses a base of 10 and the numbers are changed into hieroglyphic writings. This allowed numbers up to 1,000,000 to be expressed this way. In addition, there were also special signs for every power of 10. For example, the symbol for 1000 is a lotus flower.

Explain where and how this number system is used today.

This ancient number is no longer in use today.

What are the advantages and disadvantages of this number system?

The advantage of this system was it allowed the Egyptians to be able to express their numbers easier to add, subtract, divide or multiply. The disadvantage of this system is that it can only go up to 1,000,000 and it required a lot of space and time to write out numbers.

#exploremaths

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Donald Duck in Mathmagic Land [Adam Tan]

I feel this video didn’t specifically teach any new ideas, but rather re-enforced past lessons. As an animation targeted at a younger audience, the producer incorporated many visuals, which also succeeded in gaining my interest.

The first of the mathematical concepts we learnt in class that was explored in the video was fractals/self-similarity, and Pythagoras’ findings (at least, I think it relates to fractals). With a keen interest in music, I was surprised to find that halving a length of string brings it up an octave; ie, the ratio of a note to an octave higher is 2:1.

It was also made apparent that the golden ratio/rectangle was found in several ways in a pentagram – within the ratio of the sides, as well as the pentagon inside the pentagram.

I was told mathematics was found everywhere you look, and this statement was proven correct in this video. It was made clear that there was maths in things such as chess and sport (particularly three-cushion billiards, a sport previously unheard of to me).

The animations strongly helped me to visualise the concept of the triangle in the circle, and creating the sphere/wheel/cone.

In the end, no new lessons were taught, only varied explanations of old concepts.

#exploremaths