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Mathematics: ideas and frameworks explained

A collection of ideas, frameworks and techniques related to Mathematics, explained clearly so they are easy to understand and share.

The Mathematics of Everyday Life showing everyday maths examples including budgeting, shopping, splitting a bill, travel planning, buying a house, voting statistics, baking measurements and fitting furniture, created for the VERDI inclusive mathematics project.Mathematics in Everyday LifeLaplace's Demon thought experiment quote by Pierre-Simon Laplace about determinism and predictabilityLaplace's DemonThe Figure Skater's Spin and Conservation of Angular Momentum Illustrated with equationsThe Figure Skater's Spin and the Conservation of Angular MomentumWhat is Naismith's Rule for calculating walking time in the mountains example explained with a mountain ridge with hikers and lines for the horizontal distance and time and ascent and timeNaismith's Rule for mountain hiking timeIceberg floating orientation explained: Icebergs are usually drawn floating vertically, while a stable iceberg orientation is usually on its sideIceberg orientationWhat is parallax explanation - how parallax works showing different layers moving at different speedsParallaxA circle with a number of its mathematical parts labelled. And someone trying to climb up the tangent.Parts of a circleSneaky averages: A statistician sinking in the deep part of a pond by a sign saying the average depth is 3ftSneaky averagesMöbius strip animation: a small red ball continuously rolls around the surface of a 2-dimensional strip that has been twisted before having its ends joined - meaning the ball covers the entire shape. Möbius stripBrilliance bias: A group of people in a gallery of portraits of famous people lament that the brilliant women were forgotten againBrilliance biasFiguring out the order of operations in a calculation using BODMAS (or PEMDAS)BODMASSampling bias: a presenter proudly shows the conclusion of a bar chart of responses from people who were asked if they love responding to surveys. A resounding 'yes'.Sampling biasA breakdown of constructing the number 13 in the decimal system of base 10 next to 13 written in the base 2 of binaryBinaryThe Haversine Formula illustration: a portion of the earth's globe is shown with a green arc drawn between the cities of London, UK and Seattle, WA. The mathematical Haversine formula takes into account the curvature of the earth's surface when calculating the true distance between two points on a curved surface. The haversine formulaThe travelling salesman problem illustration showing a bewildered salesman contemplating the many options he could take to visit all the places the need across AmericaThe travelling salesman problemThe 9-times table on your Fingers illustration: holding up both hands in front of you, the example of 3 x 9 is given; whereby the 3rd finger from the left is lowered leaving 2 fingers to the left of the gap and 7 fingers to the right. 2 and 7 gives 27. The 9 times table on your fingersWhat is the coastline paradox explained - meaning the length changes depending on the size of your ruler, with Great Britain's coastline as an exampleThe Coastline ParadoxWhat makes people trust you? How to be trustworthy? The Trust Equation: Credibility, Reliability, Intimacy over Self-orientation from Charles Green at Trusted AdvisorsThe trust equationWhat's the difference between Accuracy and Precision illustrated with examples from shooting at targetsAccuracy and precisionWhat is Dunbar's number example explained: a person can't remember the name of the one person outside their circles of closer friends, super family, clan and tribe behind themDunbar’s number: 150How to fix a wobbly table by rotating itFix wobbly tables by rotatingIdempotence, or idempotent, illustrated with an idempotent action of look_at_cake that always has the same effect, compared with a non-idempotent action of eat_slice_of_cakeIdempotenceWhat is the golden ratio explained and the golden spiral and the golden ratio in faces, art, nature, architecture and how to calculate itThe Golden Ratio: Nature's Perfect ProportionsWhat is the potato radius example explained: showing a bumpy potato-like asteroid at the centre of an expanding circle and how it becomes rounder and more planet like as it gets largerThe Potato Radius: When Asteroids Turn SphericalThe Monty Hall problemAsymmetry of returnsFitts’ LawMeasures of central tendency: mean, median, modeCommon distributions: normal, skewed, paretoThe Big Data equation: big data + machine learning + cloud = informed, intelligent decisionsThe big data equationWin at MonopolyThe most beautiful equationthe Angle of Incidence equals the Angle of Reflection

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