Month: May 2015

#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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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

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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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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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

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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or confidential information or both. If you are not the intended recipient
please delete it and notify the sender.

When deciding with what mathematical concept to explain for
a 90 to 180 second video, we were having difficulties deciding on something
that we would all agree on. Then the teacher made the suggestion of doing “Clock
Arithmetic” which we settled on. We still haven’t quite worked out on how we
will present the video and still need to fill in a member with what we have
chosen…

#exploremaths

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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or confidential information or both. If you are not the intended recipient
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#exploremaths

 

For our video, Erik and I have a few topics in mind. We
though about doing it on the nature of mathematical paradoxes and we were going
to explain a few but then we developed the idea of limits and how this topic
would be ideal for a 90 to 180 second video. As for presentation, we have
thought of presenting it in ‘minutephysics-esque’ fashion by drawing out what
we are trying to explain on a whiteboard and also by simply narrating over the
images that we display on screen.

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