# Neat Math Trick



## boyntonstu (Jul 16, 2010)

A neat math trick.

All of these numbers are very easy to square (multiply by itself).

15,25,35,45,55,65,75,85,95.

First thing to remember is that all the answers end in 25.

Let's do 35 x 35.

Don't look at the 5, just the digit before 5, in this case 3.

The next digit up from 3 is 4. Multiply 3 x 4.

3 x 4 is 12. Tack on 25.

Therefore 35 x 35 is 1225. (all answers end in 25)

Next example:

45 x 45 is 2025. 4 x 5 is 20 and just tack on 25 to the 20 to get 2025.


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## Darb (Sep 14, 2010)

If I may lob a friendly but sweeping mathematical generality: with an nearly endless supply of numbers to work with, it's relatively easy to select any pattern you like, and then do an algorithmic search (or derive by hand) a subset of numbers that satisfy the desired pattern ... just for the privilege of going "ooh ah" over the seemingly magical (but mathematically hand-picked) result.

After a while, you learn to create them yourself.

_Voice of OZ: Pay no attention to that commutative law behind the curtain !







_


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## boyntonstu (Jul 16, 2010)

Darb said:


> If I may lob a friendly but sweeping mathematical generality: with an nearly endless supply of numbers to work with, it's relatively easy to select any pattern you like, and then do an algorithmic search (or derive by hand) a subset of numbers that satisfy the desired pattern ... just for the privilege of going "ooh ah" over the seemingly magical (but mathematically hand-picked) result.
> 
> After a while, you learn to create them yourself.
> 
> ...


I teach this squaring trick to 5th graders to increase their Math confidence.

I'd like to see a few of your self made tricks.


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## Darb (Sep 14, 2010)

I used to have a number of math related threads, including some math humor threads, on one of my old sites. Here's some straight math for brewing that unfortunately got corrupted during a forum software migration a few years back, so many of the equations are garbled now (lots of A-tilda's). Some of the humor threads completely disappeared, probably due to the higher incidence of symbology that didn't port over to the new platform.









Say, are you a math teacher ?

If so, it's a pleasure. I did a brief stint in Kappa Mu Epsilon's mathletes back in college, and finished with a minor in it.


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## boyntonstu (Jul 16, 2010)

Here is a very interesting geometry question that I ask my students.

Using a piece of paper, a pencil, and a ruler, draw a 4 degree angle with a 10 percent accuracy.


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## Darb (Sep 14, 2010)

boyntonstu said:


> Here is a very interesting geometry question that I ask my students.
> 
> Using a piece of paper, a pencil, and a ruler, draw a 4 degree angle with a 10 percent accuracy.


There are several ways to do it.

Here's one I cooked up off the top of my head. Many standard plastic rulers have a small hole centered in each end, enabling one to be used as an anchor and the other to scribe a circle with the tip of a pen or pencil. Accordingly:

* Use the ruler and pencil to scribe a circle on the paper. The radius is irrelevant, but the largest that will fit on the paper will make things easier.

* Keeping the original anchor point, move the other end back to the point of maximum diameter and draw a line bisecting the circle, and then place a dot at the halfway point to mark the center ... that's 180 degrees.

* Since the end of the ruler is square, place it's bottom corner on the center dot and trace the end of the ruler, then use the long side to extend the line in both directions again bisecting the circle ... that's 90 degrees.

* Use the long side of the ruler to draw a line between the ends of any 2 adjacent points on the perimeter of the circle, and then use the ruler and the same previous technique to bisect the angle facing that line ... that's 45 degrees.

* Continue the same progression forming 22.5, 11.25, 5.625, and then 2.8125 degrees.

* If you then interpolate by bisecting the difference between those last 2 angles, you get 4.21875 degrees, which is within 5.46874% of 4 degrees .. that's less than 10%.

I assume you have an easier method at the ready. The pythagorean theorem and SOH CAH TOA will probably come in handy.


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## boyntonstu (Jul 16, 2010)

Darb said:


> Here is a very interesting geometry question that I ask my students.
> 
> Using a piece of paper, a pencil, and a ruler, draw a 4 degree angle with a 10 percent accuracy.


There are several ways to do it.

Here's one I cooked up off the top of my head. Many standard plastic rulers have a small hole centered in each end, enabling one to be used as an anchor and the other to scribe a circle with the tip of a pen or pencil. Accordingly:

* Use the ruler and pencil to scribe a circle on the paper. The radius is irrelevant, but the largest that will fit on the paper will make things easier.

* Keeping the original anchor point, move the other end back to the point of maximum diameter and draw a line bisecting the circle, and then place a dot at the halfway point to mark the center ... that's 180 degrees.

* Since the end of the ruler is square, place it's bottom corner on the center dot and trace the end of the ruler, then use the long side to extend the line in both directions again bisecting the circle ... that's 90 degrees.

* Use the long side of the ruler to draw a line between the ends of any 2 adjacent points on the perimeter of the circle, and then use the ruler and the same previous technique to bisect the angle facing that line ... that's 45 degrees.

* Continue the same progression forming 22.5, 11.25, 5.625, and then 2.8125 degrees.

* If you then interpolate by bisecting the difference between those last 2 angles, you get 4.21875 degrees, which is within 5.46874% of 4 degrees .. that's less than 10%.

I assume you have an easier method at the ready. The pythagorean theorem and SOH CAH TOA will probably come in handy.








[/quote]

A radian is by definition 57.3 degrees. (Circle circumference is 2 x pi x r)

Therefore a degree is 1 part in 57.3.

....................... go out 57.3 and up 4 and you have it. (for small angles the tangent is equal to the angle)


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## Darb (Sep 14, 2010)

Yes, that's the TOA (Tangent ... Opposite over Adjacent).

Metaphorically, you took the properly paved exit, and I drove across the median ... literally.


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## whipcrackdeadbunny (May 22, 2010)

Ha! Math! I'm so bad at Math! I can barely add up the change in my pocket. It's nice to know others can enjoy it though ...


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## Darb (Sep 14, 2010)

Looks like my mad 1337 thread-killin skillz are still sharp.


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## NoSugarRob (Jun 3, 2010)

*.*


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