[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.

• 
  

[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.