Math WIZZ

[kmac]

So I just figured something out this week that shocked the heck out of me. I could not believe A} I had never noticed or figured it out before and B} That I had NEVER been taught or shown this in school or my union apprenticeship.

 

Backround: I sucked at math in school. I just never saw how I would use it or why I needed to know it. Later, after working in construction for years, I joined the union and went through the Carpenters Apprnticeship program and loved the math I learned there. I could actually see where I could use math to calculate the area of a circle...stair tread and riser ratios, roof pitch and rafter cuts....all good stuff.

I still only got the basic math needed for that and have gone no farther.

 

So a guy on another site was building a custom airbox for a 4 cylinder bike. He needed 4 1" outlets and had a 2" inlet. Almost everyone said...no no no that is not enough inlet, it will starve.

 

So since I am stuck on the couch still I decided to play a bit. I did the basic math using those diameters and Pi and found out that four 1" holes have the exact same area as one 2" hole.

 

Wow, I was shocked. Curious, I wondered is that random, like where the ratio just happeneed to intersect, OR is that a constant that stays no matter what size the circles are...DUH, it is a constant. That would have been a nice bit of info I would have liked to know over the years and possibly another reason I may have liked math as a kid.

 

If I am not clear, a circle of any given size is 4X the size as a circle exactly half of its diameter.

 

So when you have a circle and 2 circles inside that circle that intersect in the center and on the sides, it leaves you with a spade sort of shape on top and bottom, those 2 shapes are exactly the same area as the inner circles are.

 

Am I a total idiot and this is common knowledge? Or is this just a math thing that only gets taught in higher math than basic Algebra in the 9th grade {probably 4th grade now days}?

 

Feel free to bash me, I feel dumb as it is and likely deserve any butt of the joke that comes.

 

I felt pretty smart until I shared it with my Valedictorian Daughter that got 4.3 GPA in Advanced college prep math classes who laughed at me and said "duh"....deflated.

 

Poke away, I deserve it.

 

 

[Rocer]

You're too hard on yourself. Where do you think your daughter's genes, well half of them, came from? Now, get back to sewing those buttons back on your shirt after they popped off when you saw those marks along with those other shirts when you heard your daughter was to give the Valedictorian speech.

[Quinn]

This is useful knowledge when ordering pizzas.

 

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[tallman]

This is useful knowledge when ordering pizzas.

 

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BTDT

 

Ordered a 14"

 

was brought a 7"

 

they said we'll give you another 7"

 

I said "NO!"

 

bring me 3 more 7" pizzas

 

My daughters were young (about 8 and 11) at the time.

 

Manager never got it despite doing the math for himn on a na;kin.

 

Daughters did.

 

Pizza is the best example of this, IMO.

So, go big or go home.

[Danny caddyshack Noonan]

Kmac

That is why a circle and a short formula for pi was put on the plaque placed onto Voyager of some number that was going out of the solar system.

I could do arithmetic quite well when young but developed a mental block on Trig and Algebra. Later, used the heck out of it investigating crashes and working radar. Then I started teaching a couple other math blocked cops why it was simple once it was tangible.

So, before I couldn't spell rocket engineer and now I are one.

[kmac]

Tallman-

PERFECT example of WHY this is valuable information I wish I had know 30 years ago.

 

Danny-

Have you been hangin out with my dad?

That was always his saying, yesterday I couldn't spell the word, today I are one.

 

Rocer-

I did not mean to boastful about my daughter, although I am very proud of her. I was just showing that I sure missed something in school, whether of my own failings or the shortcomings of teachers at the time.

 

I have always known that 2 small circles were NOT the same as 1 double sized circle....just not that it was exactly 4 of them.

 

What ELSE DON'T I know???? Uh oh. Slippery slope there.

[tallman]

Relating to motorcycles, speed and braking have a relationship.

 

Doubling speed results in quadruple the stopping distance.

 

Like gravity and the inverse square law.

[kmac]

Would it be wierd for an almost 50 year old man to take basic math in college?

lol

[elkroeger]

Okay okay, hold on a minute.

 

How in hell do you get a 4.3 gpa on a scale that goes to 4.0?

 

I mean, good for your daughter, but somebody's makin' money on that deal, and it ain't me.

 

As far as the circles go - think about it like a plumber: two one inch pipes will fit inside of a two inch pipe (if you ignore the wall thickness). But it doesn't add up, because there's extra space outside the two one inch pipes. Incidentally, that extra space adds up to exactly 1/2 of the area of the 2" pipe.

 

What's interesting about sucking air into a motorcycle engine (or pushing water through a pipe, etc.) is that you have FRICTION, which is beyond me, but you have to oversize everything to make up for it.

 

I work with a PhD engineer, who once was explaining the number of holes I need in a screen in a fish trough at a hatchery. He scribbled down all the variables on a sheet and wrote out the equation (with friction accounted for, of course). One of the variables was the "Area of the hole" (denoted A subscript hole). When he was done with his calculations, I looked at it and said "Jesus, John. Did you just write "A-hole" in an equation?" He said "Oh, look at that I guess I did. Well, it takes one to know one."

 

I still have the A-hole equation up on my wall....

[elkroeger]

Would it be wierd for an almost 50 year old man to take basic math in college?

lol

 

get this book: Forgotten Alebra. You'll feel like a genius when you're done, and the ladies will grovel at your feet.

 

[szurszewski]

hijack

 

Okay okay, hold on a minute.

 

How in hell do you get a 4.3 gpa on a scale that goes to 4.0?

 

 

Many high school now use a weighted GPA where you get more points (4.5 or 5 depending on the system) for an A in an AP, college, honors or IB class. As far as I know, however, universities still look at the "actual" or unweighted GPAs for applicants...so, in a way, to paraphrase Nigel, it's a little bit like saying, "These go to five."

 

...please note that I am not trying to diminish the accomplishments of students who pursue those higher level classes.

[tallman]

Some are worth 6 quality points.

 

Unweighted GPA/test scores/whatchadonelatelythatsworthy/legacy/whatcharacteristicdoyahavewewant(ie linebacker/soprano/etc)

are the main criteria wrt HS to college admission.

 

Dual enrollment can getcha hs/college credit for same course

and some/many go into college as a sophomore or junior wrt credits.

 

Saves time and money.

[Joe Frickin' Friday]

One of the variables was the "Area of the hole" (denoted A subscript hole).

 

FWIW, I recently discovered that we can do subscripts and superscripts on this discussion board. The appropriate tags are sub and sup, using brackets just like you use for italicized or bolded text:

 

[sub]subscript text goes here[/sub]  [sup]superscript text goes here[/sup]

 

So:

 

A_hole = pi * R²

[Rocer]

₂^cool

 

Thanks Mitch.

[elkroeger]

Those grading scales remind me of that movie. I can't remember the name of it. The guy was all excited about his new stereo because the volume knob went to "11" instead of the usual "10".

 

"11" was somehow louder...

 

 

[Joe Frickin' Friday]

Those grading scales remind me of that movie. I can't remember the name of it. The guy was all excited about his new stereo because the volume knob went to "11" instead of the usual "10".

 

"11" was somehow louder...

 

 

Ah, a famous segment from the movie This Is Spinal Tap.

 

These go to eleven.

 

Hard to believe that's the same fellow that played Count Rugen in The Princess Bride.

[szurszewski]

Those grading scales remind me of that movie. I can't remember the name of it. The guy was all excited about his new stereo because the volume knob went to "11" instead of the usual "10".

 

"11" was somehow louder...

 

 

That is in fact the allusion I was trying to make - I guess it sort of worked.

[kmac]

Trust me, I questioned that 4.3 as well. How can a person get MORE than 100%. 100% is ALL, it is everything of that item.

Again new math I do not understand...

 

Kelsey's had to do with AP classes and college prep and also turning in non required work for extra credit. She also tutored other struggling kids in her classes. This all gave her "extra" points somehow.

 

4.0 or 4.3, she is an amazing kid that I am proud of.

 

The Spinal Tap volume 11 reference is awesome. That was one of the funniest parts of that movie.

I am a bit of a louder guy, not neccesarily obnoxious, {maybe sometimes, sorry} but I have alot of energy and tell stories exuberently....One of my riding buddy had some stickers printed up that say "Volume 11" just for me. That is my nick name with him.

 

So I think of it as not neccesarily any louder actually, but somehow "better"....lol {J/K of course I am not any better than anything}

 

Elkr, that is what I was saying exactly. I totaly understood that two 2" holes fit exactly inside of one 4" hole and had 2 spade shaped areas left over...I just did not know that those 2 spade shaped areas were exactly the same volume as the two 2" holes. Cool info...now that I am old and not likely to use it much.

 

I am also aware of the friction issue and you are better off to increase the inlet in an airbox issue, there is also turbulence and other factors. That discussion was centered on the numbers though that a 2" hole was not as big as the four 1" holes which I calculated out as the same. That is all.

 

What is the forumla for circumference?

[kmac]

Ok, I looked up circumference formula.

C=2 x pi {3.14} x R {radius} or 6.28 x R.

 

Using that formula You see that the surface area of four 1" tubes are 25.12 and the surface area of one 2" tube is only 6.28 so using a single larger diameter pipe would have dramatically less friction than using 4 smaller tubes or pipes.

 

BTW, on the air box in question, it was not long tubes of 4-1" tubes and a long 2" tube, it was more holes is sheet stock, so that may change the friction formual some.

 

So using this info that the area of four 1" holes is exactly the same as one 2" hole, but, the frisction is greater on the four 1" carbs, then, the single 2" inlet SHOULD be plenty of air to feed the four 1" carbs...right? or am I missing something?

[Antimatter]

Not to threadjack, but one of the banes of my college existence was calculus. Back when I went, it was designed as a 'cut' class to prevent those of us who were waffling about engineering from going forward. It was taught very quickly, in a crowded classroom, by a Teaching Assistant who spoke english as a 2nd language. It's always bothered me that I let it defeat me, and if anyone has a good idea for a book or series of books that would let me go back and take another crack at it, I'd appreciate it.

 

Mind you, I don't want to give the impression that I thought the TA was a bad person, but I'm pretty sure he was a math major who was naturally gifted when it came to theory, but was forced to teach the class as part of his grad student duties. As such, he was (is) probably very good at math, but not very good at teaching.

[elkroeger]

Yeah, spinal tap. that's it. groan...

 

antimatter - look up the book "forgotten calculus". That might be your ticket. Personally, I can barely do math, unless it's applied math. Indeed, I took several calc. and stats courses, but they were all applied. First, there are no engineers in there to compete against, and they dump all that theorem and proof garbage that we dim bulbs can't do. To me it's like the difference between studying piano vs. music theory.

 

I had a TA in a genetics course who would answer every question with "So what you're telling me is that you haven't read the book.". It still irritates me that I was paying tuition for that nonsense.

 

 

[RavennaAl]

This makes perfect sense. If you had a hole in the ground that was 2 feet in diameter (Hole A) and 4 smaller 1 foot diameter holes (Hole B's) even though a person would be more likely to get caught in one of the smaller holes, they most likely will remember the larger one because when you get right down to it, most people always remembers the A-Hole's they encounter

[kmac]

This makes perfect sense. If you had a hole in the ground that was 2 feet in diameter (Hole A) and 4 smaller 1 foot diameter holes (Hole B's) even though a person would be more likely to get caught in one of the smaller holes, they most likely will remember the larger one because when you get right down to it, most people always remembers the A-Hole's they encounter

 

I resemble that remark...

[BrianM]

Not to threadjack, but one of the banes of my college existence was calculus. Back when I went, it was designed as a 'cut' class to prevent those of us who were waffling about engineering from going forward. It was taught very quickly, in a crowded classroom, by a Teaching Assistant who spoke english as a 2nd language. It's always bothered me that I let it defeat me, and if anyone has a good idea for a book or series of books that would let me go back and take another crack at it, I'd appreciate it.

 

Schaum outline series work well for relearning a subject you have already taken. Also work well for additional problems/solved examples when you are taking the class.

 

You may just go to the local library and pick up a Calculus textbook and work your way through the book. Of course the book will assume you are proficient in algebra. Most students fail calculus because they are not very good at algebra, not because the concepts of calculus are very difficult.

 

[BrianM]

Relating to motorcycles, speed and braking have a relationship.

 

Doubling speed results in quadruple the stopping distance.

 

Like gravity and the inverse square law.

 

Actually, the relationship of stopping distance and speed is not an inverse square relationship. If it were an inverse relationship, as speed increased, stopping distance would decrease.

 

A car has kinetic energy. The brakes do work on the car converting the kinetic energy into thermal energy.

 

Kinetic energy = 1/2*mass*speed²

work = force*distance

 

If you assume that at maximum braking the force is at its maximum value, the braking distance is proportional to speed squared. Double your speed, speed squared increases by a factor of 4, so the braking distance also increases by a factor of 4.

[kmac]

Dang it. I started this thread out thinking I had accomplished something...now I realize I need to go back to the 3rd grade...just not sure I can fit in those little desks anymore.

[tallman]

Awware of that.

 

Why I said they had a relationship.

 

2xspeed = 4x braking distance

 

I said like gravity and Inverse Square as another example of

change that involves perception or intuition and the actual math, could have been clearer I guess.

 

Point was that most folks think two 7" pizzas would be = to a 14" pizza and that if you go twice as fast it takes twice as long to stop when it is 4 times.

Was trying to include too many examples in same train to entertain kmac.

 

[Antimatter]

Dang it. I started this thread out thinking I had accomplished something...now I realize I need to go back to the 3rd grade...just not sure I can fit in those little desks anymore.

 

I'm thinking kindergarten. I can play with paints and toys while some older woman tells me what to do. Which actually kind of describes my life now. Don't tell my wife I said that.

[kmac]

Phew,

I thought you were saying "I" belonged in Kindergarten. I mean come on, I can spell my name AND count to 20 without taking my shoes off now.

 

Although my daughter could do that in preschool...so maybe I also need Kindergarten.

 

Dang it. I gotta delete this thread before I end up back in the womb....NOBODY wants to see that.

[Quinn]

Okay, you can try to amaze your daughter by showing her how to multiply on your fingers. As an example: 6*9. Hold your hands out in front of you with all ten fingers out, palms down. Now count on your fingers starting from your left, 1, 2, 3, 4, 5, and tuck in finger number 6 (the thumb on your right hand). You've got five fingers to the left of the tuck and four to the right. Anser is 54. By the way, this only works for numbers up to ten when multiplied by nine. But you don't have to tell her that.

 

Speaking of nines, you can also tell what the remainder will be if dividing by 9 if you add the digets together and "cast off the nines." As an example, say 563/ 9. 5+6+3=14, then re-cast off 1+4=5. The remainder should be 5 for 563/9. 563/9= 62 and remainder = 5. You can actually do it a little easier by just saying (again for 563/9) 6+3=9 and "cast it off" to have just 5 remaining. The only time this is ever useful is when checking your addtion of a column of numbers. If you cast off the nines for each number, then cast them off down the column, it should give you the same remainder number as the total's. 428+691+331=1450. Casts off to be 14 (=5)+7+7=19 Cast off again = 1 and 1450 cast off =1 also. So the answer is probably correct.

 

Hope all this isn't too confusing. Next we can take up magic squares on a calculator.

 

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[kmac]

THATS IT....

{curling up in fetal position and waiting for mom to stop by}

This is gonna hurt!