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mathmajik:

MATH MYTHS: (from Mind over Math)
1. MEN ARE BETTER IN MATH THAN WOMEN. Research has failed to show any difference between men and women in mathematical ability. Men are reluctant to admit they have problems so they express difficulty with math by saying, “I could do it if I tried.” Women are often too ready to admit inadequacy and say, “I just can’t do math.”
2. MATH REQUIRES LOGIC, NOT INTUITION.  Few people are aware that intuition is the cornerstone of doing math and solving problems. Mathematicians always think intuitively first. Everyone has mathematical intuition; they just have not learned to use or trust it. It is amazing how often the first idea you come up with turns out to be correct.
3. MATH IS NOT CREATIVE.  Creativity is as central to mathematics as it is to art, literature, and music. The act of creation involves diametrical opposites—working intensely and relaxing, the frustration of failure and elation of discovery, satisfaction of seeing all the pieces fit together. It requires imagination, intellect, intuition, and aesthetic about the rightness of things.
4. YOU MUST ALWAYS KNOW HOW YOU GOT THE ANSWER. Getting the answer to a problem and knowing how the answer was derived are independent processes. If you are consistently right, then you know how to do the problem. There is no need to explain it.
5. THERE IS A BEST WAY TO DO MATH PROBLEMS.  A math problem may be solved by a variety of methods which express individuality and originality-but there is no best way. New and interesting techniques for doing all levels of mathematics, from arithmetic to calculus, have been discovered by students. The way math is done is very individual and personal and the best method is the one which you feel most comfortable.
6. IT’S ALWAYS IMPORTANT TO GET THE ANSWER EXACTLY RIGHT. The ability to obtain approximate answer is often more important than getting exact answers. Feeling about the importance of the answer often are a reversion to early school years when arithmetic was taught as a feeling that you were “good” when you got the right answer and “bad” when you did not.
7. IT’S BAD TO COUNT ON YOUR FINGERS. There is nothing wrong with counting on fingers as an aid to doing arithmetic. Counting on fingers actually indicates an understanding of arithmetic-more understanding than if everything were memorized.
8. MATHEMATICIANS DO PROBLEMS QUICKLY, IN THEIR HEADS. Solving new problems or learning new material is always difficult and time consuming. The only problems mathematicians do quickly are those they have solved before. Speed is not a measure of ability. It is the result of experience and practice.
9. MATH REQUIRES A GOOD MEMORY. Knowing math means that concepts make sense to you and rules and formulas seem natural. This kind of knowledge cannot be gained through rote memorization.
10. MATH IS DONE BY WORKING INTENSELY UNTIL THE PROBLEM IS SOLVED. Solving problems requires both resting and working intensely. Going away from a problem and later returning to it allows your mind time to assimilate ideas and develop new ones. Often, upon coming back to a problem a new insight is experienced which unlocks the solution.
11. SOME PEOPLE HAVE A “MATH MIND” AND SOME DON’T. Belief in myths about how math is done leads to a complete lack of self-confidence. But it is self-confidence that is one of the most important determining factors in mathematical performance. We have yet to encounter anyone who could not attain his or her goals once the emotional blocks were removed.
12. THERE IS A MAGIC KEY TO DOING MATH.  There is no formula, rule, or general guideline which will suddenly unlock the mysteries of math. If there is a key to doing math, it is in overcoming anxiety about the subject and in using the same skills you use to do everything else.
 Source: “Mind Over Math,” McGraw-Hill Book Company, pp. 30-43.
Revised: Summer 1999  Student Learning Assistance Center (SLAC) Southwest Texas State University
Photo: http://math2033.uark.edu/wiki/index.php/MathBusters

mathmajik:

MATH MYTHS: (from Mind over Math)

1. MEN ARE BETTER IN MATH THAN WOMEN.
Research has failed to show any difference between men and women in mathematical ability. Men are reluctant to admit they have problems so they express difficulty with math by saying, “I could do it if I tried.” Women are often too ready to admit inadequacy and say, “I just can’t do math.”

2. MATH REQUIRES LOGIC, NOT INTUITION.
Few people are aware that intuition is the cornerstone of doing math and solving problems. Mathematicians always think intuitively first. Everyone has mathematical intuition; they just have not learned to use or trust it. It is amazing how often the first idea you come up with turns out to be correct.

3. MATH IS NOT CREATIVE.
Creativity is as central to mathematics as it is to art, literature, and music. The act of creation involves diametrical opposites—working intensely and relaxing, the frustration of failure and elation of discovery, satisfaction of seeing all the pieces fit together. It requires imagination, intellect, intuition, and aesthetic about the rightness of things.

4. YOU MUST ALWAYS KNOW HOW YOU GOT THE ANSWER.
Getting the answer to a problem and knowing how the answer was derived are independent processes. If you are consistently right, then you know how to do the problem. There is no need to explain it.

5. THERE IS A BEST WAY TO DO MATH PROBLEMS.
A math problem may be solved by a variety of methods which express individuality and originality-but there is no best way. New and interesting techniques for doing all levels of mathematics, from arithmetic to calculus, have been discovered by students. The way math is done is very individual and personal and the best method is the one which you feel most comfortable.

6. IT’S ALWAYS IMPORTANT TO GET THE ANSWER EXACTLY RIGHT.
The ability to obtain approximate answer is often more important than getting exact answers. Feeling about the importance of the answer often are a reversion to early school years when arithmetic was taught as a feeling that you were “good” when you got the right answer and “bad” when you did not.

7. IT’S BAD TO COUNT ON YOUR FINGERS.
There is nothing wrong with counting on fingers as an aid to doing arithmetic. Counting on fingers actually indicates an understanding of arithmetic-more understanding than if everything were memorized.

8. MATHEMATICIANS DO PROBLEMS QUICKLY, IN THEIR HEADS.
Solving new problems or learning new material is always difficult and time consuming. The only problems mathematicians do quickly are those they have solved before. Speed is not a measure of ability. It is the result of experience and practice.

9. MATH REQUIRES A GOOD MEMORY.
Knowing math means that concepts make sense to you and rules and formulas seem natural. This kind of knowledge cannot be gained through rote memorization.

10. MATH IS DONE BY WORKING INTENSELY UNTIL THE PROBLEM IS SOLVED. Solving problems requires both resting and working intensely. Going away from a problem and later returning to it allows your mind time to assimilate ideas and develop new ones. Often, upon coming back to a problem a new insight is experienced which unlocks the solution.

11. SOME PEOPLE HAVE A “MATH MIND” AND SOME DON’T.
Belief in myths about how math is done leads to a complete lack of self-confidence. But it is self-confidence that is one of the most important determining factors in mathematical performance. We have yet to encounter anyone who could not attain his or her goals once the emotional blocks were removed.

12. THERE IS A MAGIC KEY TO DOING MATH.
There is no formula, rule, or general guideline which will suddenly unlock the mysteries of math. If there is a key to doing math, it is in overcoming anxiety about the subject and in using the same skills you use to do everything else.


Source: “Mind Over Math,” McGraw-Hill Book Company, pp. 30-43.

Revised: Summer 1999 
Student Learning Assistance Center (SLAC)
Southwest Texas State University

Photo: http://math2033.uark.edu/wiki/index.php/MathBusters

(via imathematicus)

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feellng:

The Godfather

feellng:

The Godfather

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"The only friend to walk with is one … who so exactly shares your taste for each mood of the countryside that a glance, a halt, or at most a nudge, is enough to assure us that the pleasure is shared."

CS Lewis

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inspirewerft:

geometry

(via imathematicus)

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"Which do you want: the pain of staying where you are, or the pain of growth?"

Judith Hanson Lasater

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(via backwardinduction)

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curiosamathematica:

The Wallace-Bolyai-Gerwien theorem states that any two polygons are equidecomposable: it is possible to cut any polygon into finitely many polygonal pieces and then rearrange them to obtain any other polygon.
The theorem doesn’t rely on the axiom of choice (unlike, for example, the more famous Banach-Tarski decomposition). Moreover, the decomposition and rearrangement (which consists of rotations and translations only) can by carried out “physically”: the pieces can, in theory, be cut with scissors from paper and reassembled by hand.
The problem about whether a hinged dissection exists, such as the ones in the animation, remained open until 2007. The paper Hinged Dissections Exist presents a method which always works to find a hinged dissection.

curiosamathematica:

The Wallace-Bolyai-Gerwien theorem states that any two polygons are equidecomposable: it is possible to cut any polygon into finitely many polygonal pieces and then rearrange them to obtain any other polygon.

The theorem doesn’t rely on the axiom of choice (unlike, for example, the more famous Banach-Tarski decomposition). Moreover, the decomposition and rearrangement (which consists of rotations and translations only) can by carried out “physically”: the pieces can, in theory, be cut with scissors from paper and reassembled by hand.

The problem about whether a hinged dissection exists, such as the ones in the animation, remained open until 2007. The paper Hinged Dissections Exist presents a method which always works to find a hinged dissection.

(Source: xyprogramming)

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humanoidhistory:

Happy birthday to German scientist Petrus Apianus, aka Peter Apian, born in Saxony on April 16, 1495. A mathematician, astronomer, and cartographer, he was a favorite of Charles V of the Holy Roman Empire. In 1540, Apian created Astronomicum Caesareum and dedicated it to his imperial benefactor. It was a sumptuous Renaissance instructive manual that explained, in part, how to use an astrolabe to calculate the altitude of the stars and planets. (Bibliotheque Nationale de France)

(via scientificillustration)

Quote
"One reason that people have artist’s block is that they do not respect the law of dormancy in nature. Trees don’t produce fruit all year long, constantly. They have a point where they go dormant. And when you are in a dormant period creatively, if you can arrange your life to do the technical tasks that don’t take creativity, you are essentially preparing for the spring when it will all blossom again."

Marshall Vandruff, one of the best teachers I have ever had, on artist’s block. Said during a webinar done on Visualarium to advertise his upcoming online course on animal anatomy (source links to webinar)  (via pale-afternoon)

Everyone needs to know ♥

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Said poetically.

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(Source: visualarium.com, via krbee)

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"If it is right, it happens — The main thing is not to hurry. Nothing good gets away."

John Steinbeck, born on this day in 1902, on falling in love in a magnificent letter of advice to his teenage son. (via explore-blog)

(Source: explore-blog)

Quote
"I, too, have trouble visualizing four dimensions when I’m completely sober."

— Linear algebra professor (via mathprofessorquotes)