The Presence of the Golden Ratio and the Golden Spiral throughout the World

#exploremaths

When looked at from the front, the shape of the Parthenon appears to resemble a golden rectangle. This is interesting as construction of it had completed in 438 B.C.E but it wasn’t documented by the Greeks until 300 B.C.E. Many theories for this include that, as it is present in nature, the golden ratio is aesthatically pleasing to the human eye.

 

As seen above, the Taj Mahal is also known to form a golden rectangle.

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Thankyou (By @happynikitakk)

​Hey Sir,

Just wanted to say a thank you from myself and on behalf of the rest of the class for a great course this semester. I think we have all learnt so much over the past two terms. You’ve really changed my attitude towards mathematics and I have learnt that there is more to maths than just applying formulas and difficult algebra. There were times during this semester where i had my mind blown, times when I got really excited when I solved a problem and even times when my brain hurt and I really felt like giving up. But, all in all this course has been an eye-opening experience for me and I’ve learnt a lot. I never thought i’d say this but maths can actually be fun. Thanks again!

#exploremaths

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Term 3 Summary

hourglassWe are halfway through the Exploring Mathematics course – and I hope you’ve enjoyed learning some really interesting and unusual mathematical ideas! This seemed like a good time to make sure everyone is on the same page with the current assessments that you’re all working on.

AT1: Class Discussion
At this stage in the course, you have (including today’s lesson, listed below) TEN posts that you should have written in response to concepts and work done during our lessons. Here they are for those who can’t remember:

  1. Introductory lesson
  2. The Golden Ratio
  3. 3 videos (Beauty & Mathematics)
  4. Fractals
  5. Artwork ideas
  6. Set Theory topic review
  7. Discovery or invention?
  8. Comparing the sizes of sets (rational vs. natural numbers)
  9. Division by zero (What is 0 divided by 0? How about 0 to the power of 0?)
  10. Video ideas (today’s lesson)

Please check back through all the posts and make sure you are up-to-date. Don’t forget to participate in the dialogue too by actively discussing and questioning the ideas posted by others.

AT4: Video Composition
You have already formed your groups for this, and you’ve already been issued the assessment outline. Today your task is to identify three potential ideas to make your video about and then create storyboards for each. You must then write individually about:

  • The pros and cons of each idea
  • Which idea you like best and why
  • How you (personally – not the whole group) will contribute to the project in the lead-up to submitting Stage 1 (draft)

Happy holidays everyone!

Artwork Progress (by @brendanmckee99)

I started doing a draft for my artwork, seeing how hard it is to construct a Levy Curve. The picture attached is how far I got, and is halfway through constructing another iteration of the pattern. It is just a draft version and is quite messy and not exact.

#exploremaths

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Iterated Function systems catch up (by keshini98)

I really enjoyed this lesson because we explored areas that I found very interesting. Having done functions in maths before, I thought I would be able to cope with what was happening in class. I did understand the bulk of it, but when we got to the imaginary numbers, things started to spiral out of control. Eventually, when I took another look at it, I did understand it. I have heard of imaginary and complex numbers before, and have always wanted to learn more about them. When we explored this area, I was surprised, confused yet interested at the same time.  When plotting the sets of unbounded and bounded sequences, this beautiful fractal emerged and it was a very intriguing shape. Altogether, I found this lesson very interesting.

#exploremaths

Video lesson catch up (by keshini98)

The first video (Donald Duck in Mathamagic Land) was very interesting! It discussed how Mathematics exists in everything, from galaxies to plants, animals, architecture, paintings and even music! I was surprised to hear about the mathematical logic behind the harmony of notes. The next video discussed how the Golden Ratio is evident in everything, including the proportions of our bodies. Even Ancient Greeks used the Golden Ratio in most of their architecture and sculptures. Mathematics is even evident in games such as hopscotch and chess. Overall, this ratio is really cool and seeing it in various forms is intriguing.

#exploremaths

Three Videos (by @natashaaaaaaa_xo)

Hey 🙂

All three video’s really opened my eyes, and made me realise that Math’s
is literally everywhere. The Donald Duck video was very interesting; when it
explained to us the idea that Math’s is related to music and nature. When
watching the Ted Talk video I was surprised to find that the Golden Ratio can
be found in so many places from websites to human DNA to the whole universe
itself. This idea that Golden Ratio appears in so many places really shocked
me. The third video was about Human Beauty; it questioned whether human beauty
is just about numbers. I personally don’t agree that human beauty is just about
numbers. The golden ratio cannot necessarily determine whether someone is
‘beautiful.’ Beauty does not always have to be about the physical appearance.

#exploremaths

Iterating Functions and Complex Numbers (by @iamjazzyh)

This lesson was interesting and a little confusing at the same time. I have encountered functions before however not in this area. Exploring what happened to different numbers when put into an iterating function was quite interesting. It was surprising to find that complex sets of unbounded and bounded sequences could produce, when plotted on a graph, a beautiful fractal. It was confusing at first, but the work made sense at the end. 

#exploremaths

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