A Tangible Math Lesson – Four Types of Institutional Lies

” Elitists often censor, suppress and obscure the truth, while information is removed, falsely discredited, even replaced or entirely conjured. Meanwhile, euphemisms are inserted into the wider vocabulary to steer not only people’s perceptions and decision making, but the very subjects they will reasonably consider.” – E Smith

58Despite the constraints of our educational systems, there are some excellent teachers. And there are some not so excellent instructors. We learn a lot in school, but it is also important to learn outside of school as well. Some of the most valuable lessons are not found in the teacher’s answer book, and yet some teachers operate by the book, at right angles, making no adjustments for the humanity of their students.

Not surprising given that the school system itself is geared toward creating two things: employment and expectation.

Like most people who are interested in history I dreaded math and algebra, and may actually have found my interest in history out of my disdain and fear of division and multiplication.

I remember the first time I learned how to add. I thought I had tackled the math thing then and there. I also remember the first time I was frozen in front of the class, unable to do long division on the chalkboard. And yet the mathematical lesson I have used the most since its revelation to me, and the one I remember most distinctly, turned out to be more than just a mathematical lesson.

A Tangible Math Lesson

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Understanding The Fibonacci Sequence And Golden Ratio

WakingTimes  May 30 2014

If you graph any number system, eventually patterns appear. In mathematics, numbers and their patterns do not only continue infinitely linear, but in all directions. For example, considering infinite decimal expansion, even the shortest segments have an infinite amount of points.” ~Waking Times

The Fibonacci Sequence

The Fibonacci sequence is possibly the most simple recurrence relation occurring in nature. It is 0,1,1,2,3,5,8,13,21,34,55,89, 144… each number equals the sum of the two numbers before it, and the difference of the two numbers succeeding it. It is an infinite sequence which goes on forever as it develops.

The Golden Ratio/Divine Ratio or Golden Mean

The Golden Ratio can be seen from a Chambered Nautilus to a Spiraling Galaxy
The Golden Ratio can be seen from a Chambered Nautilus to a Spiraling Galaxy

The quotient of any Fibonacci number and it’s predecessor approaches Phi, represented as ϕ (1.618), the Golden ratio. The Golden Ratio is best understood geometrically by the golden rectangle. A rectangle unevenly divided resulting into one square and one rectangle, the square’s sides would have the ratio of 1:1, and the new rectangle would be exactly proportionate to the original rectangle – 1:1.618.

This iteration can continue both ways, infinitely. If you plot a quarter circle inside each of the squares as they reiterate, the golden spiral is formed. The golden spiral is possibly the most simple mathematic pattern that occurs in nature like shells of snails, sea shells, horns, flowers, plants. Numbers are only what we use to organize quantitative information. Continue reading

Is The Universe Made Of Math? [Excerpt]

ScientificAmerican  January 10 2014

Excerpted with permission from Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, by Max Tegmark. Available from Random House/Knopf. Copyright © 2014.

basketballWhat’s the answer to the ultimate question of life, the universe, and everything? In Douglas Adams’ science-fiction spoof “The Hitchhiker’s Guide to the Galaxy”, the answer was found to be 42; the hardest part turned out to be finding the real question. I find it very appropriate that Douglas Adams joked about 42, because mathematics has played a striking role in our growing understanding of our Universe.

The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: with mathematics. Galileo famously stated that our Universe is a “grand book” written in the language of mathematics. So why does our universe seem so mathematical, and what does it mean? In my new book “Our Mathematical Universe”, I argue that it means that our universe isn’t just described by math, but that it is math in the sense that we’re all parts of a giant mathematical object, which in turn is part of a multiverse so huge that it makes the other multiverses debated in recent years seem puny in comparison.

Math, math everywhere!

But where’s all this math that we’re going on about? Isn’t math all about numbers? If you look around right now, you can probably spot a few numbers here and there, for example the page numbers in your latest copy of Scientific American, but these are just symbols invented and printed by people, so they can hardly be said to reflect our Universe being mathematical in any deep way.

Because of our education system, many people equate mathematics with arithmetic. Yet mathematicians study abstract structures far more diverse than numbers, including geometric shapes. Do you see any geometric patterns or shapes around you? Here again, human-made designs like the rectangular shape of this book don’t count. But try throwing a pebble and watch the beautiful shape that nature makes for its trajectory! The trajectories of anything you throw have the  same shape, called an upside-down parabola. When we observe how things move around in orbits in space, we discover another recurring shape: the ellipse. Moreover, these two shapes are related: the tip of a very elongated ellipse is shaped almost exactly like a parabola, so in fact, all of these trajectories are simply parts of ellipses.

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