[MATHS] Leonhard Euler, Königsberg bridge, Traversable Networks.

 

Leonhard Euler (pronounced Oiler) (15 April 1707 - 18 September 1783) was a swiss mathematician, physicist, and one of the founders of pure Mathematics. In 1720, he enrolled at University of Basel at age 13. 

He solved the Basel Problem in 1734 which earned him recognition in the mathematical world.

In 1737, he published Mechanica which describes the mathematics governing movement. In 1734, he released Introductio in Analysin Infinitorum which deals with the analysis and studying mathematical functions through infinite processes.

Euler died from a brain haemorrhage on 18 September 1783 in Saint Petersburg, Russia, aged 76. 

Bridges of Königsberg.

Mathematician Carl Gottlieb Ehler grew interested in the islands and bridges of Königsberg and asked: "Which route would allow someone to cross all seven bridges without crossing any of them more than once?"

Euler's solution:

Euler came up with a theory that applies to graphs with two or more nodes. An Eulerian path is only possible when:

1. When there are exactly two nodes of odd degree where one of the odd nodes is the starting point and the other is the endpoint.

2. All nodes are of even degree, the Eulerian path will start and end at the same location. This is also called the Eulerian circuit.

Traversable Networks

A network is traversable when we can find a route through the network along the edges and uses all the edges only once.

Rules for a Network to be traversable:

1. The network must be fully connected.

2. All vertices (nodes) are of even degree or there are exactly two nodes of odd degree and the rest are of even degree.

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[MATHS] Shapes and terminologies.

A shape is any plane figure with side and/or vertices.

A quadrilateral is a four-sided figure whose internal angles are 360 degrees. 

A square is a quadrilateral that has four equal sides and four equal angles. The diagonals of a square bisect each other and the opposite sides of the square are parallel.

A rectangle is a four-sided shape where the opposite sides are parallel and of equal length.  The diagonals of the rectangle also bisect each other. 

A parallelogram is a quadrilateral where both pairs of opposite sides are equal. Its opposite sides and angles are congruent. Each diagonal of a parallelogram separates into two congruent triangles. A parallelogram is a convex polygon (interior angles less than 180 degrees.)

A rhombus has four equal sides, the diagonals of the square are perpendicular and bisect the opposite angles. Its vertices are not 90 degrees. The rhombus is not a cyclic quadrilateral (vertices lie on a single circle.)

PROPERTIES OF QUADRILATERALS:

1. Opposite sides are equal.

2. Opposite sides are parallel.

3. Opposite angles are equal.

4. Sum of two adjacent angles is 180 degrees.

5. Diagonals bisect each other.

[ESOL] 2020 Reflection

The first few weeks of school have been quite rough for me because my mental and physical health deteriorated. During my break in school, I always think about how am I going to catch up with my tasks in school and how am I going to prepare myself for my upcoming assessments. On days I am able to complete the whole school day, I would always do the task as much as I can but I know it would somehow be not enough. I know that I should strive better when my health is in good condition, and do what I can when my health hinders me to do so much work. Right now, I want to do whatever I can to catch up and so far my performances have been okay. I still hope for recovery physically and mentally!

[ESOL] Goals for 2020.

My goals from 2019 haven't changed a bit and are still the same goals I want to aim for this year.

Academically, I want to learn more and encounter my weaknesses in different fields. I want to take care more of myself to be healthier when it comes to practical work such as music and drama. I want to be more mentally prepared for my assessments and stay calm in every situation. I also want to learn about failing, I want to learn more from my mistakes and use them to improve my strategies, academically and in real life. I also hope for mental recovery. 

[ESOL] Matariki - Short Reading Response

Title of Book: Matariki

Author: Waitangi Teepa

Genre/Text Type: Informative

Date Read: 19th February 2020

This text was about Matariki, a group of seven stars. Matariki is also the alternative name for the
Maori New Year. 

I chose to read this text because I am very interested in astrology. It also gives me more information about
Maori culture.

One interesting feature was how the stars appear for most of the year but disappear in late Aprils and
return somewhere between May and June.

A quote/evidence that shows this is “You can see the stars of Matariki for most of the year, but they
disappear in the night sky of Aotearoa in Late April. The stars appear again in winter (in late May or early
June). This means that the star of Matariki disappears for a short while and appears again in winter.
Matariki is also the time where we cherish our time with our loved ones and leave everything that hurts and
burdens us behind.

This interests me because there is astrology to explain how the stars of Matariki disappear and appear for a
particular time. It also shows how we all connect to each other and learn moral values as this event passes.

I can relate to the main characters' ways of celebrating Matariki by being with my own family and reflect on my own actions as a person. I fully relate because I was raised family-oriented and being good and forgiving because we are all capable of doing wrong.

The characters remind me of everyone who is with their families, physically or not. We are all connected with each other through our values, beliefs, and similarities. We also share a culture that everyone has a tradition of celebrating or following.

Hopelessly Devoted to You - Music Solo Performance Evaluation

I really enjoy music ever since I first held a microphone as a kid, it played a very big role in my life and in my family! This year's music class is one of my favourite subjects because this class helps me develop myself as a musician and a student. The classroom just casually became my natural habitat, I didn't mind showing what I really and what potentials I can show in terms of music. The performances I've delivered two times this year helped me develop my skills more and had a little realisation about my own abilities.
For my first solo performance, I performed Hopeless Devoted To You by Olivia Newton-John from Grease. This piece was recommended by my itinerant vocal teacher, Barb. I haven't watched the musical but this song is one of my grandmum's favourite songs and the lyrics of the songs was something I used to relate to, being hopelessly devoted to someone I didn't have, someone who had me deciding whether to continue admiring them or to just give it up. It was a fond memory of mine, so it helped me to deliver the song well.
There were a few struggles while during practice. The song was familiar to me but I never got to listen to it as a whole. Memorising the lyrics took me a while because I had so many things to do that I didn't have enough time to know the whole words. The technique I used to deliver the song was a bit... off. Barb had pointed out some of my weak points in singing and she helped me to improve those areas which were successful after a few sessions of practices.  I used to think that being a good singer was all about having powerful performances, having a strong stage presence and ability to reach very high notes. In my case, it became a mindset to me which didn't help me improve at all. Hearing the same feedback about my singing being strong used to give me a confidence boost because of that wrong mindset I've sunk in my brain. That changed when we had our practice performance and read Mr Sloan's feedback.  It made me realised that even a few practices, I still perform but having difficulties enjoying the actual performance. It had me thinking that I perform because I want to achieve a certain technique, but not finding myself in the song even though it was a song that helped me relate to someone and myself in the past.  I'm thankful for Mr Sloan for his honest feedback because it was something I've been looking for in my past performances other than hearing the same response over again. After that, I want more honest feedback and point out my weaknesses because I know it will help me to become a better singer. I would also like to thank Barb for helping me to improve and I'm still improving so I'm becoming more welcome to receive more honest criticisms!
I got excellence for this performance and I felt relieved because the reflections I've made and the help from my teachers' efforts to help me were all paid off. This performance really helped me to find what were the things I lacked and still lacking. It was really worth it after all the hard work.
I don't really have songs to choose yet because I'm thinking of a concept of songs that are different from the songs I usually sing. It's better to keep it a secret first because who knows? I might surprise you next time. :)

ORIGINAL PIECE:

MR. SLOAN'S FEEDBACK!

PERFORMANCE LINK: https://drive.google.com/file/d/1dQ2kM-PeDYAZBTYJr52yUgTep5_-jjOo/view

The South Island Robin research reflection.

I started to do my research on Monday in preparation for my research reflection in ESOL.

I've looked at two websites to gather information about the South Island Robin, Notornis and Nzbirdsonline. I found out that the South Island Robin is a native bird in New Zealand with the size of a sparrow, they are 18 centimetres in length and 35 grams in weight. They have a few differences in their appearances by gender: the male robin is a dark-grey black over their head, neck, mantle and upper chest. Their flight feathers are brownish black.  Their lower chests and bellies' colour is white to yellow with a sharp differentiation between black and white on the chest part. Meanwhile, the females are light to grey in the upper body. Their bellies and chest area are smaller, having less distinction between grey and white feathering.
They use specific hunting methods at different times of the year. They use scanning, hawking (hunt on the wing for food) and flycatching (the method of catching flies) during late November and December. They use hawking and flycatching during January to mid-March and hawking during the late summer. During this part of the research, it was my first time encountering the words hawking and flycatching.
The robins live in mature forests, scrubs and exotic plantations. They also prefer moist areas with plants growing underneath forest canopies.
South Island Robins are monogamous, having only one partner in breeding. Their breeding seasons starts from July to March and they lay their eggs from July to December.
They are decreasing in population due to predators like rats, stoats and feral cats and loss of habitat. The robins have been tried to translocate where there are no predators, the translocation caused the inbreeding, cause problems to reproduction and have genetical consequences.