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Solve ANY Math Problem! - Braintenance

On April 24, 2012 By // No comments:

You can solve any math problem if you know the formula (i.e., the proven shortcut to arriving at the answer without the need for giant chain calculations).

These formulas are like keys to unlocking the secrets of arithmetic and mathematical puzzles and riddles.

The tougher issues are those of knowing how to conduct a search (knowing the right search engine parameters to enter (hint: a Google search might be a good idea for your first pass at "asking a question" without asking a question) and finding the right formula to apply.

This process sharpens your mind in that it requires that you 1) identify the problem; 2) formulate a question; 3) construct an efficient search engine query; and 4) glance through at least a small number of sites or articles about the issue which you want to address.

Every one of these steps ratchets up a whole menu of cognitive skills to a higher level.

Solving the problem is merely the proverbial icing atop the cake [an inexcusably cheap metaphor, but it was better than "the last nugget squeezed atop the mountain," which I was told not to use as it might prove unsavory to my readers of delicate constitution and discerning taste.

Here are several quick problems which you can solve by merely asking using the problem/ question/ search query/ cursory reading approach described above:

A) What is the sum of the whole numbers from 1 to 5,000, inclusive?

B) What is the product of all of the whole numbers from 1 to 25, inclusive? {This number is often expressed as 25! or '25 factorial'}

C) What is the number (a constant) to ten decimal places obtained by dividing any circle by its diameter?

D) How many Angstrom Units are there in twelve inches (one foot)?

E) How many possible combinations of 3 partner groups can be created out of a total classroom of 30 students?

Make me proud! Wrinkle those brains! Expand those minds! Sharpen those skills!

Douglas E Castle for The Braintenance Blog

p.s. Please view The Twitterlinks Hubspot Blog for access to a list of terrific Twitter streams on a variety of topics well worth following. Sometimes, we even follow you back...

I Will Teach You Nothing - You Will Learn Much From Me

On December 03, 2011 By // No comments:

Portrait of René Descartes, dubbed the "F...

Image via Wikipedia - Rene Descartes: philosopher, mathematician, theoretical physicist, and a fellow with an unkempt but nonetheless fascinating hairstyle.

Most individuals don't actually understand the distinction between teaching (a third-person exercise) and learning (a first-person exercise).

When a wise philosopher [most philosophers are assumed to be wise -- this is principally out of respect, I believe, for any person with the wondrous ability to a) survive without actually having to either earn a living by some sort of work, or b) with the good fortune to be leisurely whittling away at a substantial familial inheritance while pontificating about whatever happens to be on his or her mind] said to one of his disciples (every successful philosopher worth his weight in either hemlock or horse manure must have disciples):

"I will teach you nothing. And you will learn much from me," he was not even stating a clever paradox. There actually is no puzzle or riddle embedded in this preliminarily conflictory-seeming statement. If you don't quite understand why, re-read the first sentence of this post.
If that doesn't satisfy, read on:

We learn by teaching ourselves. No one truly teaches us. We learn by voluntary applying our senses and ability to reason to teaching ourselves. This is what is meant when someone (usually a meddlesome, conceited, self-proclaimed "adult") says,"You can best teach by example," or "children don't learn by what we preach to them; they learn by observing what we actually do."

A teacher is a catalyst, or a source of information, or an inspiration. But we learn by teaching ourselves.

Douglas E. Castle [http://TwitterLinksHubspot.blogspot.com]

Expand Your Mind: Pattern Recognition

On September 30, 2011 By // No comments:

Your mental capacity, plasticity, memory, recall and deductive reasoning are all dramatically enhanced by your ability to recognize patterns and to extrapolate (or generalize) from them. In some cerebral circles, the NICs (nerds-in-charge) refer to this phenomenon as "learning a rule." This notion has great applicability in the world of artificial intelligence (AI), but it is the shining key to a means of improving our own intelligence as well as increasing the actual speed of thought. Imagine being able to think faster because you are able to make 'connections' more rapidly? This skill is valuable to cultivate. Not surprisingly, it is a skill that can be improved by simple exercise.

Pattern recognition skills are involved in every aspect of gaming, athletics, problem-solving and life. The more different (and complex) patterns that we are able to recognize from prior exposure, the easier and faster it will be for us to recognize new patterns. By the way, simple analogies actually involve pattern recognition. To illustrate, in solving the analogy query that follows, an association between things (associations are the building blocks of patterns) is necessary for us to get the right answer:

Horrible but memorable analogy, with multiple choice possibilities:

Fahrenheit is to Temperature, as...

a) Tuna is to Fish;
b) Oral is to Rectal;
c) Length is to Height;
d) Celsius is to Cold;
e) Inches is to Length;
f) Pitney is to Bowes;
g) Antihistamine is to Allergy;
h) Wet is to Rain.

The correct answer, of course, is choice e) Inches is to Length. The reason is that Fahrenheit is a means of measuring Temperature, and Inches is (are) a means of measuring Length.

Perhaps it's time for some practice. If you'll complete the sequences below (i.e., find the next item in each of the series), I promise that I'll have the answers for you by Monday this coming. These don't involve word-based analogies -- they are simply series of numbers. Do these - they're as stimulating as they are beneficial...

Incidentally, I dedicate this post to Technorati 4F3BBD7YKWFZ.

A) 1, 3, 6, 10, 15, ?

B) 1, 1, 2, 3, 5, 8, 13, ?

C) 1000, 0100, 0010, 0001, 1000 ?

D) 1, 4, 9, 16, 25 ?

E) 200, 3000, 40000, 500000, ?

F) 1, 100, 2, 99, 3, 98, 4, ?

G) 1.21, 2.32, 3.43, 4.54, ?
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That's all for now, fellow (and lady) Braintenance Buffs. We'll compare our answers on Monday.

Douglas E Castle [http://aboutDouglasCastle.blogspot.com]

TechnoratiMedia - http://technoratimedia.com/

Solve ANY Math Problem! - Braintenance

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I Will Teach You Nothing - You Will Learn Much From Me

Expand Your Mind: Pattern Recognition

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