Online Mathematics tutoring Ballarat in Ballarat, Victoria | School

Online Mathematics tutoring Ballarat

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24.01.2022 Coronavirus is spreading exponentially, which means that the rate is the highest. Please take it seriously. There used to be a mathematical theory of 6 handshakes in 1920s. So called SIX DEGREES OF SEPARATION, the idea that all people are six, or fewer, social connections away from each other. I suppose, today, as the population is bigger (appproximately10 billion), the number of handshakes is around 11. In other words you are only 11 handshakes away from an infected Itali...an or Iranian. This theory is real. our world is small, which was proved experimentally. The small-world experiment comprised several experiments conducted by Stanley Milgram and other researchers examining the average path length for social networks of people in the United States. Milgram's study results showed that people in the United States seemed to be connected by approximately three friendship links, on average, without speculating on global linkages; he never actually used the phrase "six degrees of separation". See more

23.01.2022 Imagine 2020 is not a year but a rugby score, as is scrawled below. This score spells out a word. Can you work out which one? UPD: Just rotate the image ninety degrees anti clockwise.

22.01.2022 Parker (a company that produces pens) ran an advertising campaign in the early 70s simply showing a hand using a Parker Pen to write out the following 'mathematical' formula: (3.5G + V/2)/4(H2O)3 + 3(360o) = M Apparently they received thousands of letters from frustrated chemists, mathematicians and physicists, all informing them that the formula was nonsense. As it turns out, formula is a Martini formula: 3.5 shots of gin and half a shot of vermouth over 4 parts (H2O)^3 (ice...Water cubed), then three stirs (the 3*360degrees) and...Hey presto! The campaign (which ran in Newsweek and Time) received one very critical letter asking "Who ever heard of Martini without an olive?".

22.01.2022 An absolute value of sadness.

22.01.2022 Frightening density of formulas

21.01.2022 The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It may have been originally named the Kleinsche Fläche ("Klein surface") and then misinterpreted as Kleinsche Flasche ("Klein bottle"), which ultimately may have led to the adoption of this term in the German language as well. A Klein Bottle, although it is a closed surface with no edge, does not enclose any volume. Ignoring the thickness of the walls, the glass Klein Bottles have zero volume because they do not divide the universe into an inside and an outside. They have no boundary. A very interesting illustrative video is in the first comment.

20.01.2022 How can someone born in 2020 be older than someone born in 2019? Roughly how many people will fall into this category this year? That is, how many babies born in 2020, if any, will be older than at least one person born in 2019? Solution: If someone is born, say, at 1am in the morning of January 1 2020 in Sydney, then everyone born in the UK in the afternoon of December 31 2019 will be younger than them but born the previous year.... In fact, the number of people born in 2020 who are older than someone born in 2019 is going to be in six figures. About 360,000 people are born every day. (Most in Asia). A child born in French Polynesia between 10pm-midnight on Dec 31 2019 will be younger than all the Jan 1 2020 births until that moment, i.e until 6pm in Beijing, 3.30pm in Delhi, and so on. A fair estimate is probably about half of 360,000. A person thinking out of the box: Anyone born in 2020BC will be older than anyone born in 2019AD! (Source: https://www.theguardian.com/science)

18.01.2022 Be careful with what you wish for! Merry Christmas!

16.01.2022 So we call pi an irrational number. You can’t represent the exact value of pi as a fraction made up of two whole numbers, such as 2/3 or 18/11. But the earliest mathematicians, who had no clue about the existence of irrational numbers, didn’t get much beyond representing pi as 25/8 (the Babylonians, about 2000 B.C.) or 256/81 (the Egyptians, about 1650 B.C.). Then, in about 250 B.C., the Greek mathematician Archimedesby engaging in a laborious geometric exercisecame up w...ith not one fraction but two, 223/71 and 22/7. Archimedes realized that the exact value of pi, a value he himself did not claim to have found, had to lie somewhere in between. Given the progress of the day, a rather poor estimate of pi also appears in the Bible, in a passage describing the furnishings of King Solomon’s temple: a molten sea, ten cubits from the one brim to the other: it was round all aboutand a line of thirty cubits did compass it round about (1 Kings 7:23). That is, the diameter was 10 units, and the circumference 30, which can only be true if pi were equal 3 Excerpt from Death By Black Hole: And Other Cosmic Quandaries Neil deGrasse Tyson

16.01.2022 You might have heard the expression that to a topologist, a donut and a coffee cup appear the same. In many branches of mathematics, it is important to define when two basic objects are equivalent. In graph theory (and group theory), this equivalence relation is called an isomorphism. In topology, the most basic equivalence is a homeomorphism, which allows spaces that appear quite different in most other subjects to be declared equivalent in topology. The surfaces of a donut and a coffee cup (with one handle) are considered equivalent because both have a single hole. https://www.facebook.com/photo.php?fbid=3198513493600471&set=gm.2555864738058908&type=3&theater

15.01.2022 When I was at Los Alamos I found out that Hans Bethe was absolutely topnotch at calculating. For example, one time we were putting some numbers into a formula, and got to 48 squared. I reach for the Marchant calculator, and he says, That’s 2300. I begin to push the buttons, and he says, If you want it exactly, it’s 2304. The machine says 2304. Gee! That’s pretty remarkable! I say. Don’t you know how to square numbers near 50? he says. You square 50that’s 2500and s...ubtract 100 times the difference of your number from 50 (in this case it’s 2), so you have 2300. If you want the correction, square the difference and add it on. That makes 2304. Excerpt from Surely You’re Joking, Mr. Feynman: Adventures of a Curious Character Richard Phillips Feynman

13.01.2022 Cool mathematical facts

10.01.2022 Silly mathematical mnemonics

09.01.2022 Mathematical drama!

08.01.2022 The BanachTarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them without changing their shape. However, the pieces themselves are ...not "solids" in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces. A stronger form of the theorem implies that given any two "reasonable" solid objects (such as a small ball and a huge ball), the cut pieces of either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox". The reason the BanachTarski theorem is called a paradox is that it contradicts basic geometric intuition. "Doubling the ball" by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought, intuitively speaking, to preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes. However, this is not applicable here because in this case it is impossible to define the volumes of the considered subsets. Reassembling them reproduces a volume, which happens to be different from the volume at the start.

08.01.2022 For more than a thousand years, one of the world's major population centers used these symbols for addition: someone walking toward you (and so was to be "added" to you), and someone walking away from you (for subtraction). These Egyptian symbols could easily have spread to become universally accepted, just as other Middle Eastern symbols had done. Phoenician symbols, for example, were the source of the Hebrew and - aleph and beth and also the Greek and alpha and betaas in our word alphabet. Excerpt from E=mc2 David Bodanis

06.01.2022 Guilty as charged

06.01.2022 Conservation of thoughts are valid in classical, relativistic, and quantum theory. Symmetries and conservation of thoughts are the two fundamentals laws of ancient mantra systems. Amit Ray, Mantra Design Fundamentals - Basics of mantra forms, structures, compositions, and formulas

03.01.2022 The Möbius strip is a surface with only one side and only one boundary component (edge). A line drawn starting from the seam down the middle will meet back at the seam but at the "other side". If continued the line will meet the starting point and will be double the length of the original strip. Escher created a few art pieces based on the concept of the Möbius strip. Here is Escher‘s Möbius Strip II, depicting nine ants trapped in an endless march around a möbius grid. The second picture shows how to make a Möbius strip, which is, in fact, not exactly a strip.

01.01.2022 Thinking hurts sometimes.