Motorway Problem

How to choose the shortest road that connects several towns. This is a story about local and global minimums. Excellent presentation  of soapy films.

Advertisements

Unrepresentative Voting

Leslie Green explains how our voting systems can be unrepresentative.

z8587

Five different parties are standing in an election for one representative. The voting  methods:  First past the post (FPTP): the party with the highest vote-count wins.

Is the voting system representative?

The no-pets party has 30% of the total, whereas parties that want pets are the remaining 70%.  As it stands the FPTP system would vote-in the no-pets party, which does not represent the view of the electorate.  What has happened is that the pro-pet movement has splintered, dividing the vote. In order to overcome this, one can use a transferable vote scheme so people can vote for their preferred option safely, preventing the hated no-pets party from winning.

A more detailed analysis can be found in an example.

First Woman to Win the Abel Prize

Karen Uhlenbeck to win the most prestigious award in mathematics – the Abel Prize.

Uhlenbeck

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, USA.

Her theories have revolutionized our understanding of minimal surfaces, such as those formed by soap bubbles.

Niels Henrik Abel (1802–1829) was a Norwegian mathematician. In spite of his short life, he made significant contributions to a variety of mathematical fields.

Big Ben Maths

Big Ben is the nickname for the Great Bell of the clock at the north end of the Palace of Westminster in London, United Kingdom.  bigben

A pile of old coins helps to keep the clock mechanism accurate.  The pennies are stacked on the pendulum of the clock and have acted as weights. Adding or taking away coins effects the pendulum’s centre of mass and the rate at which it swings. A single penny will change the clock’s speed by two fifths of one second per day.

How does the weekly time change if we add 5 pennies to the pendulum?

Answer

At twelve o’clock, twelve chimes  ring from the great bell in 44 seconds. ## How long does it takes to ring the hours at 15:00 ?

Answer

Singapore Math

pay-3456736_1280

Singapore math  is a teaching method based on the national mathematics curriculum used for kindergarten through sixth grade in Singapore. Singapore math, also known as the “mastery approach”: students learn a specific concept  in a linear progression before moving to the next more complex subject. Students learn and master fewer mathematical concepts at greater detail using a three-step learning process: concrete, pictorial, and abstract. These are techniques of the teaching methods: to cover fewer topics in greater depth, handling objects such as pencils, dice, or paper clips, pictorial visualisation by drawing diagrams, bar modelling (a pictorial method used to solve arithmetic problems). Bar modelling is far more efficient than the “guess-and-check” approach. A 2015 study of 140 schools in the UK by found that the mastery approach improved the speed at which students learned math skills.

This is how Jeff Bezos, the richest man on the planet teaches maths to his children.

 

 

Math Symbols

We use math symbols to express complex mathematical texts in a shorter form.

=   replaces   “is equal to

+ replaces “and

×   replaces   “multiplied by

. . . .

There are many Greek symbols like   π ∑   and special symbols like   √ ∞ ∈   in mathematics.

John David Walters explains where math symbols come from in the video:

A Self-educated Mathematician Established the Boolean Algebra

George_Boole

George Boole (1815–1864)

The term “Boolean algebra” honors George Boole (1815–1864), a self-educated English mathematician. Boolean algebra captures essential properties of both set operations and logic operations. Boolean logic is credited with laying the foundations for the information age (computers and cell phones).

One of the puzzles on Boolean logic:

There are three balls X, Y and Z. They are colored red, white and blue, but not necessarily in this order. One, but only one, of the following statements is true:

X is red

Y is not red

Z is not blue

3 balls
How many solutions does the puzzle have?

Think yourself before checking the solution.