Dear Sir,
\nI would like to find the meaning of the bizarre arithmatic symbols, like: * # and many others I do not how to write it on an e-mail.<\/p>\n<\/blockquote>\n
This is a great question since bad math notation is one of the reasons math appears confusing for many people, and causes unnecessary math anxiety.<\/p>\n
Asterisk and other signs for multiplication: <\/b> The cross sign for multiplication (×) was suggested by the Englishman William Oughtred (1574-1660). <\/p>\n
Gottfried Leibniz (1646-1715, the German who developed calculus) rightly objected to the cross because it can easily be confused with the letter \"x\", which of course is used a lot in math (and which should be typed using Times New Roman font and use italics, like this x<\/i><\/span>, but unfortunately, not enough teachers or book publishers do this, adding to students' confusion). <\/p>\n The \"times\" sign, or cross (×) is commonly used in England and Commonwealth countries. <\/p>\n Leibniz proposed the dot (. or more commonly the \"mid dot\", ·) for multiplication and this is used throughout the USA and Europe. (Leibniz also suggested the \"cap\" symbol (∩) for multiplication. It also has the meaning of \"intersection\" in set theory.) <\/p>\n Unfortunately, the dot is also used for the decimal point, so if we see \"5·3\" we should take this to mean \"5 times 3\", while \"5.3\" is \"5 (decimal) point 3\". In Europe it is common to use comma (,) for the decimal point, so 3·2,5 would mean \"3 times 2 point 5\". This is a little better than if we use dots for both: 3·2.5.<\/p>\n It's all rather silly and confusing.<\/p>\n There is a branch of math where cross product<\/b> is different from dot product<\/b>. You can read more here: Dot product of 2 Vectors<\/a><\/p>\n The asterisk<\/b> (*, from the Latin which means \"little star\") is used in computer programming for multiplication. For example a*b means \"a multiplied by b\". (It is also used as a \"wild card\" character, for example *.jpg will find all image files with a \"jpg\" extension when doing a search.)<\/p>\n Perhaps we should use the asterisk for multiplication in math, too. It is easy to read, easy to type and probably not as prone to confusion as the dot and the × symbols.<\/p>\n The # (\"hash\", \"number sign\" or \"pound sign\"):<\/b> This symbol also suffers from inconsistent naming and use. According to Wikipedia<\/a>:<\/p>\n The mainstream use in the U.S. as follows: when it precedes a number, it is read as \"number\", as in \"a #2 pencil\" (spoken aloud as: \"a number two pencil\"); however, when it follows a number it is read as \"pounds\" referring to the unit of weight, as in \"5# of sugar\" (spoken aloud as \"five pounds of sugar\").<\/p>\n<\/blockquote>\n This one is not so common in Commonwealth countries, except as a symbol on your telephone.<\/p>\n We should try to simplify and standardize the symbols used in mathematics. Many symbols are used differently in different countries, and often one symbol is used for more than one purpose, and vice-versa. <\/p>\n You may also be interested in Towards more meaningful math notation<\/a>.<\/p>\n A lot of the time we look at math from a very narrow point of view. Usually we are concerned with the current chapter in our textbook only and have little idea where the math comes from or how it fits into the greater scheme of things.<\/p>\n I've been reading The Math Gene<\/i> by Keith Devlin. In this book, he argues that humans developed the \"math gene\" (not a real one, he means the ability to do math) at the same time we developed language. He also believes all people can \"do math\".<\/p>\n He has a neat way of describing how math developed through history. The answer to \"what is mathematics?\" is constantly evolving.<\/p>\n So mathematics was essentially about numbers.<\/p>\n Mathematics was the study of numbers and shape during this period.<\/p>\n Mathematics became the study of numbers, shape, motion, change and space.<\/p>\n The answer to \"what is math\" had become numbers, shape, motion, change, space and the mathematical tools that are used in this study. Whole new branches of math have appeared, like topology, complexity theory, dynamical systems theory, chaos theory and many sub-branches of probability and disaster prediction. Climate change has triggered new interest in modeling and the idea that small inputs can have huge effects.<\/p>\n So a simple answer for the question \"what is mathematics?\" is that it's the study of patterns. Not just patterns that you see in your carpet or on wallpaper, but patterns in numbers, hierarchies, geometry, language, traffic, algebra, the universe, and so on.<\/p>\n We're all able to spot patterns and to see when a pattern is broken. In fact, that's an important part of being human and for survival. So essentially, we are all mathematicians!<\/p>\n A poll on IntMath through October asked readers:<\/p>\n During weekends, how many hours do you spend doing math homework (or study)?<\/b><\/p>\n Poll results:<\/p>\n 32% 4 or more hours Total votes: 2100<\/b> Now, this was an interesting result for me because I know most people do ZERO math on weekends. How do I know? <\/p>\n We can learn a lot from people's behavior on the Web. From their searches in Google, Yahoo or Bing we can see what they really want to know. And from the pages they visit on the Web, we can see where their search took them. How long they stay and how many pages they look at gives us a good indication of what really interests them.<\/p>\n This graph shows total visitor traffic on Interactive Mathematics<\/a> from Aug to Oct 2009. This is why I asked that question in the poll and why I am surprised at the result.<\/p>\n I wrote an analysis of this and some other interesting \"math on the Internet\" trends in the following special article:<\/p>\n Who studies math on weekends?<\/a><\/p>\n There's a lot of interesting real-life math involved in Global Information Systems (GIS), including 3-D Earth Geometry<\/a>.<\/p>\n Next week is GIS Day, which aims to increase \"geographic literacy\". From the GIS Day site<\/a>:<\/p>\n GIS Day is playing a powerful role in creating geographic awareness throughout our world.<\/p>\n GIS Day provides an international forum for users of geographic information systems (GIS) technology to demonstrate real-world applications that are making a difference in our society.<\/p>\n More than 80 countries will participate in holding local events such as corporate open houses, hands-on workshops, community expos, school assemblies, and more.<\/p>\n<\/blockquote>\n You can participate at your school or community center. You can get free materials from the site as well. What you learn could help reduce some of the destruction to our planet.<\/p>\n a) Who studies math on weekends?<\/a> b) Friday Math Movie - Did You Know 4.0<\/a> c) Making math accessible for the blind<\/a> d) MoreNewMath - funny equations about life<\/a>\n
2. Math tip (b) \u2013 What is mathematics?<\/h2>\n
![\"arithmetic](\"\/blog\/wp-content\/images\/2009\/11\/subtraction.gif\" "\\"arithmetic")
Before 500BC - Arthmetic:<\/b> Math was mostly about numbers and arithmetic. Ancient Egyptian, Babylonian (present-day Iraq) and Chinese mathematics concerned itself with how to combine numbers. It arose from the simple needs of commerce - weighing, counting, measuring, and determining profit.<\/p>\n![\"Euclidean](\"\/blog\/wp-content\/images\/2009\/11\/geometry.gif\" "\\"Euclidean")
Between 500 BC and 300 AD - Geometry:<\/strong> The ancient Greeks were very interested in geometry. This was the time of Pythagoras, Euclid and Archimedes, where they tried to solve problems in geometry and ran into some very challenging problems (like what is the value of √2, when you don't believe in irrational numbers? This number appeared when they tried to find the diagonal of a 1×1 square).<\/p>\n![\"newton's](\"\/blog\/wp-content\/images\/2009\/11\/newton-apple.gif\" "\\"newton's")
The 17th century - study of motion and change:<\/strong> Newton (in England) and Leibniz (in Germany) independently developed calculus. This gave a massive impetus for the scientific and engineering achievements of the industrial revolution. It also meant travel by ship became a lot safer and this spurred exploration like never before.<\/p>\n![\"fractal](\"\/blog\/wp-content\/images\/2009\/11\/fractal.gif\" "\\"fractal")
End of the 19th century - tools of math:<\/strong> By the mid-18th century, mathematics took on more of a life of its own, rather than as the supporting cast for physics and the other sciences. There was more interest in studying mathematical phenomena for their own sake.<\/p>\n3. Latest IntMath Poll - Weekend math study<\/h2>\n
\n22% None
\n20% 1 hour
\n17% 2 hours
\n10% 3 hours<\/p>\n
\nPoll date: Oct 2009<\/b><\/p>\n![\"google](\"\/blog\/wp-content\/images\/2009\/11\/google-analytics-intmath.gif\" "\\"google")
<\/p>\n4. GIS Day on 18 Nov<\/h2>\n
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5. From the math blog<\/h2>\n
\n How many students do math homework on the weekends? What caused this spike in search traffic? [This article was mentioned earlier.]<\/p>\n
\nHere's an update to the excellent \"Shift Happens\" movies.<\/p>\n
\nThe abacus is a useful tool for helping blind people to learn math.<\/p>\n
\nHere are some funny and thought-provoking equations explaining life's experiences.<\/p>\n