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Topics - jas_fluidm

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16
Hadith / pail of water problem
« on: April 27, 2013, 12:32:13 PM »
There are 6 pails, 3 of the pails are filled with water. Can you move only one pail and make a pattern of: full pail, empty pail, full pail, empty pail, full pail, empty pail?

Solution to Pails of Water:
Pour all of the water from the 2nd pail into the fifth pail.

17
Hadith / simple basic math problem of the day
« on: April 27, 2013, 12:26:26 PM »
In a musical talent show, there were 65 participants. At the end of first round, ten participants with the following roll numbers were selected for the final - 6, 14, 34, 17, 24, 62, 52, 50, 18, 20. If Sophia's number was announced four numbers before the last number, what was her roll number?

19
Faculty Sections / Math in the Medical World
« on: April 20, 2013, 03:37:36 PM »

Max Little is an applied mathematician who developed a voice analysis software for Parkinson's disease screening. The Parkinson's Voice Initiative asked for volunteers to recite simple vocal sounds over the phone which were recorded for further analysis. This algorithmic software has a 98.6% accuracy rate in detecting Parkinson's disease. Though it is not yet an official method of diagnosis, its cost effectiveness, simplicity in screening, and ability to reach a large population make it very promising.

21
Departments / Life of Pi
« on: April 19, 2013, 03:41:03 PM »
The number π (/paɪ/) is a mathematical constant that is the ratio of a circle‘s circumference to its diameter, and is approximately equal to 3.14159. It has been represented by the Greek letter “π” since the mid-18th century, though it also sometimes written as pi. π is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers (such as 22/7 or other fractions that are commonly used to approximate π); consequently, its decimal representation never ends and never repeats. Moreover, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge. The digits in the decimal representation of π appear to be random, although no proof of this supposed randomness has yet been discovered.

Pi-unrolled-720.gif

 

Life of Pi is a movie by Ang Lee about the stories of a boy, Piscine, who suffered verbal abuse in school because his name was often taken to be “Pissing”.

In an effort to move beyond this, he makes a huge effort to become known as Pi by going up to the blackboard in every class he attends and explaining the meaning of Pi. This culminates in his final class, Math, where he proceeds to write down from memory the first 10,000 digits of pi spread over 5 blackboards. From then on he is known as Pi.

Why did Ang Lee cast Gerard Depardieu in a bit part in the movie?

Because of piscine on the plane!

Pi is usually recalled as being either 22/7 or 3.14. Various methods have been used to remember more digits.

Cadaeic encompasses the first 7 digits. c=3,a=1 etc

The phrase “How I need a drink,alcoholic, of course. After all those lectures involving radical equations” will get you 15 digits. How=3,I=1,need=4 etc.

March 14th has been known as Pi day. 3-14…


source: http://getaftermath.com/blog/life-of-pi/

22
Departments / Logical-Mathematical Intelligence – Defined
« on: April 16, 2013, 05:58:55 PM »

Logical-mathematical intelligence is the biological computational capacity that relates to reasoning, logic and abstract thinking. Children who favor  a logical-mathematical intelligence will tend to be quite skilled with numbers and numerical concepts, drawn to problems of logical complexity and scientific reasoning.

To be clear, the fact that a child may exhibit a tendency towards one particular intelligence is not to say that they don’t exercise other intelligences. Nor does this mean that only those kinds of individuals that are “mathematical” have logical-mathematical intelligence. Rather, we all have the ability to engage our various intelligences in different ways and under varying circumstances. What matters is that we expose ourselves to opportunities that will allow us to develop our different intelligences and that we are mindful of the way in which we (and our children) process the diverse information which we encounter throughout our day.

With that in mind, the following list offers various tasks and activities designed to help children develop their logical-mathematical intelligence.
Activities

The activities are presented in levels of increasing complexity. These levels are in no way related to a child’s age or grade level. Rather, in light of the fact that each child has a unique intelligence profile, these activities allow children to start at whatever level they prefer and to continue feeling engaged and motivated in this learning experience as they advance to the more challenging levels. Also, in addition to logical-mathematical intelligence, many of these activities also help develop other intelligences. In those instances, I have identified the relevant intelligences using the MI code outlined here.

Please note that this list is neither absolutely comprehensive nor is it intended to be used as a checklist of performance. These are simply suggestions to help stimulate the development of your child’s intelligence. With that in mind, I welcome feedback and additional suggestions.

LEVEL 1

    Record stories told to you by someone else and use your notes as a basis for a story. Identify the key elements and create an outline of the story. [L.I.]
    Collect a variety of leaves and classify them in five different ways. [N.I.]
    Practice adding, subtracting and dividing using raisins, buttons or other objects.

LEVEL 2

    Make a puzzle. [S.I.]
    Create a maze or crossword puzzle for a friend. [S.I.]
    Listen to patterns in music. [M.I.]
    Gather random assortments of items from your house and arrange them in a pattern. Then sort or categorize them in different ways. Chart the results and explain them with a friend. [S.I.][Ie.I.]
    Measure different things with your various body parts. Compare the lengths of different items in your house. [BK.I.]
    Predict the ending of a book you are reading. [L.I.]
    Map out the main ideas and sub-points of each idea from a book you are reading. Think of a new story and map out the main ideas and sub-points of each main idea for your new story. [L.I.]
    Create new riddles and share them with your friends. [L.I.]
    Write directions for completing a task and then give them to someone else. Discuss how effective the directions were in helping the other person complete the tasks. [L.I.][Ie.I.]
    Think of a problem you are currently facing and illustrate a machine that you would create to help you solve the problem. [S.I.]
    Create patterned number sequences and have someone else identify the pattern. Try creating patterns with shapes or words as well. [L.I.][S.I.]

LEVEL 3

    Create a secret code and write it down in a code key format. Write letters using your code key. Share your code key with someone else and see if they can decipher your message. [L.I.][S.I.][Ie.I.]
    Choose one of your favorite books and write the next episode or continuation of the story. [L.I.]
    Pick a topic to discuss and find arguments to support both sides. Have a debate with someone else. Give each other feedback about the strengths and weaknesses of the arguments. [L.I.][Ie.I.]
    Find examples of history “repeating itself” or think of a time when the same mistake has been made multiple times. Reflect upon why this is and how those mistakes could have been avoided. [Ia.I.]
    Follow a recipe to make a cake from scratch. Illustrate the recipe. [L.I.][S.I.][BK.I.]
    Create a dance using ten different dance steps. Teach the dance to a friend. [BK.I.][Ie.I.]
    Create a “paint by numbers” picture for someone else to color. [S.I.]
    Make a calendar and keep track of important events. [L.I.][S.I.]
    Take a walk and notice patterns in nature.  [N.I.]

Source:http://totthoughts.com/2012/02/28/activities-logical-mathematical-intelligence/


23
Departments / use your intelligence and write a problem to work out
« on: April 16, 2013, 05:43:39 PM »

Your brain needs exercise just like a muscle. If you use it often and in the right ways, you will become a more skilled thinker and increase your ability to focus. But if you never use your brain, or abuse it with harmful chemicals, your ability to think and learn will deteriorate.

Here are 5 simple ways anyone can squeeze a bit more productivity out of the old gray matter.

1. Minimize Television Watching – This is a hard sell. People love vegetating in front of the television, myself included more often than I’d like. The problem is watching television doesn’t use your mental capacity OR allow it to recharge. It’s like having the energy sapped out of a muscle without the health benefits of exercise.

Don’t you feel drained after a couple hours of TV? Your eyes are sore and tired from being focused on the light box for so long. You don’t even have the energy to read a book.

When you feel like relaxing, try reading a book instead. If you’re too tired, listen to some music. When you’re with your friends or family, leave the tube off and have a conversation. All of these things use your mind more than television and allow you to relax.

2. Exercise – I used to think that I’d learn more by not exercising and using the time to read a book instead. But I realized that time spent exercising always leads to greater learning because it improves productivity during the time afterwards. Using your body clears your head and creates a wave of energy. Afterwards, you feel invigorated and can concentrate more easily.

3. Read Challenging Books – Many people like to read popular suspense fiction, but generally these books aren’t mentally stimulating. If you want to improve your thinking and writing ability you should read books that make you focus. Reading a classic novel can change your view of the world and will make you think in more precise, elegant English. Don’t be afraid to look up a word if you don’t know it, and don’t be afraid of dense passages. Take your time, re-read when necessary, and you’ll soon grow accustomed to the author’s style.

Once you get used to reading challenging books, I think you’ll find that you aren’t tempted to go back to page-turners. The challenge of learning new ideas is far more exciting than any tacky suspense-thriller.

4. Early to Bed, Early to Rise – Nothing makes it harder to concentrate than sleep deprivation. You’ll be most rejuvenated if you go to bed early and don’t sleep more than 8 hours. If you stay up late and compensate by sleeping late, you’ll wake up lethargic and have trouble focusing. In my experience the early morning hours are the most tranquil and productive. Waking up early gives you more productive hours and maximizes your mental acuity all day.

If you have the opportunity, take 10-20 minute naps when you are hit with a wave of drowsiness. Anything longer will make you lethargic, but a short nap will refresh you.

5. Take Time to Reflect – Often our lives get so hectic that we become overwhelmed without even realizing it. It becomes difficult to concentrate because nagging thoughts keep interrupting. Spending some time alone in reflection gives you a chance organize your thoughts and prioritize your responsibilities. Afterwards, you’ll have a better understanding of what’s important and what isn’t. The unimportant stuff won’t bother you anymore and your mind will feel less encumbered.

I’m not saying you need to sit on the floor cross-legged and chant ‘ommm’. Anything that allows a bit of prolonged solitude will do. One of my personal favorites is taking a solitary walk. Someone famous said, “All the best ideas occur while walking.” I think he was on to something. Experiment to find the activity that works best for you.

Conclusion – I hope you aren’t disappointed that none of the techniques I’ve proposed are revolutionary. But simple, unexciting answers are often the most valid. The challenge is having the will to adhere to them. If you succeed in following these 5 tips, you’ll be rewarded with increased mental acuity and retention of knowledge.

If you’re still hungry for more, check out the follow up post: 5 More Ways to Make the Most of Your Intelligence.

source: http://www.pickthebrain.com/blog/5-simple-ways-to-make-the-most-of-your-intelligence/

24
Science Discussion Forum / a problem and solution
« on: April 11, 2013, 04:01:41 PM »
A parking lot contains 80 vehicles. Each vehicle is either a car or a truck, and each vehicle is either red or green.  35 vehicles are red, and 60 vehicles are cars. If there are 9 green trucks, how many red cars are there?
sol: 80-60=20
      20-9=11
      35-11=24
hence ans is 24.

25
Science and Information / Re: How-google-works
« on: March 16, 2013, 03:48:14 PM »
thanks for this post

26
Science Discussion Forum / New math concept.
« on: March 13, 2012, 04:16:03 PM »
New Mathematics or New Math was a abbreviated, dramatic change in the way mathematics was learned in American grade schools, and to a lesser extent in European countries, during the 1960s.

New Math underlined mathematical structure through abstract concepts like set theory and number bases other than 10.

Other topics introduced in the New Math include modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra. Most of these topics (except algebraic inequalities) have been greatly de-emphasized or eliminated since the 1960s.

Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic. The material also put new demands on teachers, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies.

In the Algebra preface of his book Precalculus Mathematics in a Nutshell, Professor George F. Simmons wrote that the New Math produced students who had "heard of the commutative law, but did not know the multiplication table."

One Example of New approach:

A "New Math Way" is to not only learn how to accomplish subtraction by regrouping in the normal decimal system, but learn it in base 8 as well.

    Base 8: regrouping the eights column means adding eight to the ones column and subtracting one from the eights column

        i.e. 342 − 173 = 147.



27
Science Discussion Forum / a Simple Probability problem
« on: March 08, 2012, 11:08:05 AM »
A university admitted 100 students who transferred from other institutions. Of these students, 34 transferred from two-year community colleges, 25 transferred from private four-year institutions, and the rest transferred from public four-year institutions. If two different students are to be selected at random from the 100 students, what is the probability that both students selected will be students who transferred from two-year community colleges?

Answer:
34/100 * 33/99 = 1122/9900 = 17/150

Another way to solve this problem:

Total combinations of 2 students from 2-year community colleges: 34!/(2!(32!)) = 561

Total combinations of 2 students from all 100 students: 100!/(2!(98!)) = 4950

Then the probability is 561/4950 = 17/150

28
Science Discussion Forum / Simple basic math problem
« on: March 08, 2012, 11:03:06 AM »
a manager is forming a 6-person team to work on a certain project . from the 11 candidates available for the team , the manager has already chosen 3 to be on the team , in selecting the other 3 team members , how many different combinations of 3 of the remaining candidates does the manager have to choose from ?

answer:
There are only 8 people left to choose from, so 8C3 = 8! / (3! * 5!) = (8*7*6*5*4*3*2*1)/(3*2*1*5*4*3*2*1) = (8*7*6)/(3*2*1) = 56

29
Science Discussion Forum / Area of regular polygon
« on: March 05, 2012, 07:55:18 PM »
The formulae below give the area of a regular polygon. Use the one that matches what you are given to start. They assume you know how many sides the polygon has. Most require a certain knowledge of trigonometry.

area= N*s^2/4*tan(180/N)
 where
S  is the length of any side
N  is the number of sides
TAN  is the tangent function calculated in degrees

Note: Unlike a regular polygon, unless you know the coordinates of the vertices, there is no easy formula for the area of an irregular polygon. Each side could be a different length, and each interior angle could be different. It could also be either convex or concave.
 
One approach is to break the shape up into pieces that you can solve - usually triangles, since there are many ways to calculate the area of triangles. Exactly how you do it depends on what you are given to start. Since this is highly variable there is no easy rule for how to do it.

30
Science Discussion Forum / Earliest mathematicians
« on: March 05, 2012, 03:45:29 PM »
Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic. The markings include six prime numbers (5, 7, 11, 13, 17, 19) in order, though this is probably coincidence.

The advanced artifacts of Egypt's Old Kingdom and the Indus-Harrapa civilization imply strong mathematical skill, but the first written evidence of advanced arithmetic dates from Sumeria, where 4500-year old clay tablets show multiplication and division problems; the first abacus may be about this old. By 3600 years ago, Mesopotamian tablets show tables of squares, cubes, reciprocals, and even logarithms, using a primitive place-value system (in base 60, not 10). Babylonians were familiar with the Pythagorean theorem, quadratic equations, even cubic equations (though they didn't have a general solution for these), and eventually even developed methods to estimate terms for compound interest.

Also at least 3600 years ago, the Egyptian scribe Ahmes produced a famous manuscript (now called the Rhind Papyrus), itself a copy of a late Middle Kingdom text. It showed simple algebra methods and included a table giving optimal expressions using Egyptian fractions. (Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. To divide 17 grain bushels among 21 workers, the equation 17/21 = 1/2 + 1/6 + 1/7 has practical value, especially when compared with the "greedy" decomposition 17/21 = 1/2 + 1/4 + 1/17 + 1/1428.)

While Egyptians may have had more advanced geometry, Babylon was much more advanced at arithmetic and algebra. This was probably due, at least in part, to their place-value system. But although their base-60 system survives (e.g. in the division of hours and degrees into minutes and seconds) the Babylonian notation, which used the equivalent of IIIIII XXXXXIIIIIII XXXXIII to denote 417+43/60, was unwieldy compared to the "ten digits of the Hindus."

The Egyptians used the approximation π ≈ (4/3)4 (derived from the idea that a circle of diameter 9 has about the same area as a square of side 8). Although the ancient Hindu mathematician Apastambha had achieved a good approximation for √2, and the ancient Babylonians an ever better √2, neither of these ancient cultures achieved a π approximation as good as Egypt's, or better than π ≈ 25/8, until the Alexandrian era.

reference: http://fabpedigree.com/james/mathmen.htm

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