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I'm trying to layout the six sided shape shown to roughly the same proportions. I know I want the top to be .5" per side and the height (of the side, not the complete shape) to be 6". The bottom dimension would be somewhere around 2" but what is the formula for figuring out the exact dimension? I would work it out by trial and error except I have several of various sizes to layout.Thanks for any help,Doug
Reply:The bottom can be anything you want (less than 12.5 in). Itll just change the angle of the sides and the overall height of the finished piece.Sent from my iPhone using Tapatalk
Reply:Pythagorean theorem; x squared + y squared = h squared.Works for right triangles.SOHCAHTOA. sine = opposite/hypotenuseCosine = adjacent/hypotenuseTangent= opposite/adjacent.
Reply:Thanks! That's kind of what I thought but when I tried one with a 2.75" base by the time I got around they were not matching up, probably due to poor layout. I'll give it another try.
Reply:Thanks el perro. A bit beyond my skills but I do want to learn more math so I'll research more. How do you apply these formulas to non-triangles?
Reply:This is quite simple, just draw a hexagon that is the size that you want the base to be, and that will give you the measurementsAlso when dealing with trapezoidal shapes just cut them into triangles that makes the math easier.What do you mean they didn't match up? What material are you working with?
http://www.philswelding.com
Reply:For non-triangles it works by drawing triangles where you need them.Then the straight sections between are rectangles.Dave J.Beware of false knowledge; it is more dangerous than ignorance. ~George Bernard Shaw~ Syncro 350Invertec v250-sThermal Arc 161 and 300MM210DialarcTried being normal once, didn't take....I think it was a Tuesday.
Reply:
Originally Posted by MetalMan23
This is quite simple, just draw a hexagon that is the size that you want the base to be, and that will give you the measurementsAlso when dealing with trapezoidal shapes just cut them into triangles that makes the math easier.What do you mean they didn't match up? What material are you working with?
Reply:There are online calculators.http://www.1728.org/quadtrap.htm
Reply:
Originally Posted by doug_w
I cut out a test piece in cardboard and taped them together. When I taped the first to the last it didn't sit flat but like I said they probably weren't very accurate. The final will be 12 or 14 gauge steel.
Reply:I cant wait for opus to enlighten us on this...Miller Dynasty 280 DX, Lincoln 210 MP
Reply:
Originally Posted by doug_w
I cut out a test piece in cardboard and taped them together. When I taped the first to the last it didn't sit flat but like I said they probably weren't very accurate. The final will be 12 or 14 gauge steel.
Reply:I would cut the pieces out of a sheet like this, https://uploads.tapatalk-cdn.com/201...0da972241a.jpg
http://www.philswelding.com
Reply:The easiest and stupidest (no pun intended) is to take a 2' square and drawn a 90* angle on the table in soapstone. Then draw a vertical line 1/4" away. This gives you 1/2 of your top width. Then take a compass and set it to 6" and put it in the end of the 1/4" mark. Now draw a arc. Anywhere on that arc is where it can be. Now pull off the original square line and you can get all your measurements.Sent from my 2PS64 using Tapatalk
Reply:Thanks for everyone's help. Was pretty easy once I got my layout more exact. Ended up laying them out like you suggested metalman. Tacked in pairs then tacked the pairs together. Took a little nudging to get the last ones line up.
Reply:Looks good from here!
Reply:very good job.i.u.o.e. # 15queens, ny and sunny fla
Reply:Excellent
Dave J.Beware of false knowledge; it is more dangerous than ignorance. ~George Bernard Shaw~ Syncro 350Invertec v250-sThermal Arc 161 and 300MM210DialarcTried being normal once, didn't take....I think it was a Tuesday.
Reply:Handy trig calculator for future reference/bookmarking:http://www.carbidedepot.com/formulas-trigright.aspI use it all the time...
Reply:I think the thing is that this trig **** is a little intentionally overcomplicated so that regular folks can't learn it. I'll do my best to explain. I tutor kids in math to get money for welding supplies. You can think of this sin cos tan **** as just random names like bill joe and ty. The important thing to know is that they are ratios like 3 apples to 2 oranges as a 3" side to 2" side in a triangle. You remember the ratios by some indian chief who was actually a relative of geronimo. He is called soh cah toa. Sin (angle) = opp/hyp (soh). Cos (angle) = Adj/hyp (cah). Tan (angle) =Opp/Adj (toa). Basically you feed it an angle for lunch and it will crap out the ratio of the sides as a decimal. If you take tan(45 degrees), it will crap out 1. Which means the opposite and the adjacent side are each 1 unit. You can think of hyp or hypotenuse is the fattest mutant side of a triangle. Adj. is the side that's hugging the angle while also not the fattest side. And Opposite is the side that is directly opposite. So lets say we have a have a road that starts at sea level and goes on with a 26 degree grade that goes for 10 miles via the mile markers. We want to know A: how many miles up in elevation are we. We know the angle, 26 degrees. We know the hypotenuse, 10 miles. But we don't know the X axis length, or the adjacent. And we don't know the Y axis length, the opposite. So we smartly pick the sin ratio. not cos or tan as it won't work. sin(26 degrees) = opp/hyp which is sin(26) = elevation/10miles. We type in sin(26) into our calc and we get 0.43. Make sure that you calc is in degree mode. That means the opp side is 0.43 units and the hyp is 1 unit. The problem is we arent done. We don't know what 1 unit equals. It could mean years till i die or how bad your wife drives. But since we know its 10 miles we are all safe and alive. Since these are all ratios. we say 0.43unit/1unit = elevation/10miles. By solving for elvation we get 4.3. So our elevation is 4.3 miles. To calculate the angle based off the elevation and road mile markers you cant use sine. You need to use arcsin. The sin function eats an angle and poops out a ratio. The arcsin function eats an angle and craps out a ratio. Another name for arcsin is sin^-1. The calculator labels it sin^-1 to cut printing costs and to save letters. The arc sin function is the exact opposite of the sin function. They are the ying and the yang. So you run arcsin(ratio)=angle so arcsin(4.3 opposite/10 hyp) and we get arcsin(0.43) which equals 25.46 degrees. The reason its not exactly 26 degrees is because i rounded the 4.3 instead of 4.3blahblachblach. To get more precision use more decimal places. Hope this helps. BTW I am not bad at math and blah at welding. If you are in NJ NY PA area, I can teach you all the layout trig geo math as well as a few tricks and short cuts like if a wire spool's cable is rolled out how much feet is it or if a spring is uncoiled how long it really is in simple terms in exchange for welding lessons. Doc Welder? I NEED WELDING HELP LOL, I LITERALLY CANT TEACH MY SELF. CANT KEEP A STEADY HAND. CheersLast edited by n00b; 11-30-2018 at 09:58 PM.
"It's always SPOOOOOOKY Season."
NJ- "Its only illegal if you get caught" - Chinesium welder Yoda: Overlord of Magic Smoke, I am
Reply:
Originally Posted by doug_w
Thanks for everyone's help. Was pretty easy once I got my layout more exact. Ended up laying them out like you suggested metalman. Tacked in pairs then tacked the pairs together. Took a little nudging to get the last ones line up.
Reply:
Originally Posted by n00b
I think the thing is that this trig **** is a little intentionally overcomplicated so that regular folks can't learn it. I'll do my best to explain. I tutor kids in math to get money for welding supplies.
Reply:Math is easy once you can get someone to explain it to you in simple terms,
http://www.philswelding.com
Reply:
Originally Posted by MetalMan23
Math is easy once you can get someone to explain it to you in simple terms,
Reply:
Originally Posted by n00b
I think the thing is that this trig **** is a little intentionally overcomplicated so that regular folks can't learn it. I'll do my best to explain. I tutor kids in math to get money for welding supplies. You can think of this sin cos tan **** as just random names like bill joe and ty. The important thing to know is that they are ratios like 3 apples to 2 oranges as a 3" side to 2" side in a triangle. You remember the ratios by some indian chief who was actually a relative of geronimo. He is called soh cah toa. Sin (angle) = opp/hyp (soh). Cos (angle) = Adj/hyp (cah). Tan (angle) =Opp/Adj (toa). Basically you feed it an angle for lunch and it will crap out the ratio of the sides as a decimal. If you take tan(45 degrees), it will crap out 1. Which means the opposite and the adjacent side are each 1 unit. You can think of hyp or hypotenuse is the fattest mutant side of a triangle. Adj. is the side that's hugging the angle while also not the fattest side. And Opposite is the side that is directly opposite. So lets say we have a have a road that starts at sea level and goes on with a 26 degree grade that goes for 10 miles via the mile markers. We want to know A: how many miles up in elevation are we. We know the angle, 26 degrees. We know the hypotenuse, 10 miles. But we don't know the X axis length, or the adjacent. And we don't know the Y axis length, the opposite. So we smartly pick the sin ratio. not cos or tan as it won't work. sin(26 degrees) = opp/hyp which is sin(26) = elevation/10miles. We type in sin(26) into our calc and we get 0.43. Make sure that you calc is in degree mode. That means the opp side is 0.43 units and the hyp is 1 unit. The problem is we arent done. We don't know what 1 unit equals. It could mean years till i die or how bad your wife drives. But since we know its 10 miles we are all safe and alive. Since these are all ratios. we say 0.43unit/1unit = elevation/10miles. By solving for elvation we get 4.3. So our elevation is 4.3 miles. To calculate the angle based off the elevation and road mile markers you cant use sine. You need to use arcsin. The sin function eats an angle and poops out a ratio. The arcsin function eats an angle and craps out a ratio. Another name for arcsin is sin^-1. The calculator labels it sin^-1 to cut printing costs and to save letters. The arc sin function is the exact opposite of the sin function. They are the ying and the yang. So you run arcsin(ratio)=angle so arcsin(4.3 opposite/10 hyp) and we get arcsin(0.43) which equals 25.46 degrees. The reason its not exactly 26 degrees is because i rounded the 4.3 instead of 4.3blahblachblach. To get more precision use more decimal places. Hope this helps. BTW I am not bad at math and blah at welding. If you are in NJ NY PA area, I can teach you all the layout trig geo math as well as a few tricks and short cuts like if a wire spool's cable is rolled out how much feet is it or if a spring is uncoiled how long it really is in simple terms in exchange for welding lessons. Doc Welder? I NEED WELDING HELP LOL, I LITERALLY CANT TEACH MY SELF. CANT KEEP A STEADY HAND. Cheers
Originally Posted by docwelder
noob; i didn't have the patience to wade through your long post until now. thanks for the math help offer but i got through almost 50 years of weld/fabrication with my shaky math skills so i figure i can struggle through the next fifty. if we can work out logistics i'll be more than glad to help you out. shoot me a pm and we'll go from there.
Reply:lol. not really agree there minessota dave. I know its not that hard espc with practice and real world use. hell i had to use this trig crap, some thing called law of cosines to cut out some sections of pipe for a pillowblock bearing. but i think the way its taught, its an abstraction that can't really be intuitively realized. Most kids forced to memorize unit circle and arbitrary crap and are forced to write their answers in radians rather than degrees which again is an abstraction as we dont think in radians as human beings as 1 radian is about 57.blah blah degrees. We get that the idea is you cut up a circle into 3 slices and have .14 left over and the degree of each slice is a radian but its stupid. Plus its taught without/ expl. how it relates to the graphs and triangles as you have to figure that out yourself.Last edited by n00b; 12-03-2018 at 10:51 PM.
"It's always SPOOOOOOKY Season."
NJ- "Its only illegal if you get caught" - Chinesium welder Yoda: Overlord of Magic Smoke, I am
Reply:Here is the "finished" project for my class. Thanks again for the help. Went together pretty easy once I got going.
Reply:
Originally Posted by n00b
lol. not really agree there minessota dave. I know its not that hard espc with practice and real world use. hell i had to use this trig crap, some thing called law of cosines to cut out some sections of pipe for a pillowblock bearing. but i think the way its taught, its an abstraction that can't really be intuitively realized. Most kids forced to memorize unit circle and arbitrary crap and are forced to write their answers in radians rather than degrees which again is an abstraction as we dont think in radians as human beings as 1 radian is about 57.blah blah degrees. We get that the idea is you cut up a circle into 3 slices and have .14 left over and the degree of each slice is a radian but its stupid. Plus its taught without/ expl. how it relates to the graphs and triangles as you have to figure that out yourself.
Reply:So are mortar bases, and all that's necessary to make a fun day is an Officer who fails to learn a radian is not a degree.
Reply:
Originally Posted by MinnesotaDave
You completely miss the point of geometry and trigonometry if you think it's an abstraction.I introduce trig with an exercise of drawing right triangles by some ratios of side lengths. Students pick the ratios they want to draw.Then they measure the angles and label them (all on large poster board).Then they present their findings to the other groups.After, they decide how come the same ratios, but different side lengths, ended up with the same angles (plus/minus some drawing error).Then we use the trig tables (not calculators yet).Trig is easier for students after the discovery exercise.My entire knowledge base of real life examples (not the crap in the book) is always used in trig, geometry, algebra, calculus and applied calculus.People who insist on memorization, and/or students who prefer to memorize instead of think, are doing it wrong.Btw, military scopes are in radians.
Reply:
Originally Posted by William McCormick
To me if you simplify each task that you need to do in a shop to build just about anything, you often need to do a very little measuring, almost never need to know what the angle is, and you hardly ever use math, especially any Trig to build almost anything you can imagine. Now I think the original poster, could not conceive that no matter what size he made the two ends of his octagon shaped pyramid/plateau that they would line up. He kind of suspected it because he mentioned his original cuts were not that good and was going to try it again. But none of that had to do with math. Metalman caught it right away and offered the proper information because he is hands on. I think the basics are often overlooked, like someone trying to figure out what the angle for an octagon is and not just dividing up 360 degrees to find out. In a metal shop you often just cut out the top and bottom octagon if only out of some 26 gauge to see what is going on. From there you can measure the difference in radius from flat to flat of each octagon and come up with the angle based on the height by drawing out a simple triangle. But you never do it with math or angles. I love gadgets more than anyone but rarely can I even use a calculator for much. I use cadd only because it saves me from laying out on a table. But the amount of math that is going on to do that layout in cadd is almost mind-boggling. So it is only because it is hiding all that math that I use it. I can only use it because I do understand it. It is a paradox. I wrote some of the formulas that are used in my cadd program so I understand them but I cannot even remember them. Haha. Sincerely, Wiliam McCormick
Reply:High school math was Hell! My first year algebra teacher wasn't well. He had a psychotic breakdown before the year ended, then we had a series of babysitters as substitutes. Little learning took place. Second year it was geometry. I had a great teacher. We connected. Also, it was a non abstract subject. The whole thing was intuitive.Algebra II was a nightmare! Teacher (1971-2) was flamboyantly gay. I was not as enlightened as now. If he hadn't been gay I'd have hated him, and that gave me an extra reason. First day he told the class "I want you to call me Dudley. ........Don't fall behind. If you are having any trouble, come to me."Third day I knew I was in trouble. It wasn't making sense. After school, I went to him. There was a line of students ahead of me. I waited my turn, then approached his desk. With open book in hand, I said:"Dudley, I don't....." He cut me off in mid sentence, "To you, I'm Mr. Hopkins!" I turned, and left the room. Nothing improved. We openly acknowledged our mutual dislike. Although little learning took place, I passed with a C average.\Senior year, no change, same teacher, same relationship. He clicked with the clique of "IN" students, I sat in the back of the room, bored.Math for me has been Geometry, and whatever I have picked up after high school. I believe learning in school is like a chain, no stronger than its weakest link. Both student, and teacher must contribute.An optimist is usually wrong, and when the unexpected happens is unprepared. A pessimist is usually right, when wrong, is delighted, and well prepared.
Reply:Using a compass and a little math:Hexagon inscribed in a circle:https://www.mathopenref.com/constinhexagon.htmlSlant height of a cone:https://www.mathopenref.com/coneslantheight.htmlAddendum: Truncated cone slant height:https://math.tutorvista.com/geometry...of-a-cone.htmlLast edited by Denis G; 01-08-2019 at 11:06 AM.
Reply:
Originally Posted by MinnesotaDave
You completely miss the point of geometry and trigonometry if you think it's an abstraction.I introduce trig with an exercise of drawing right triangles by some ratios of side lengths. Students pick the ratios they want to draw.Then they measure the angles and label them (all on large poster board).Then they present their findings to the other groups.After, they decide how come the same ratios, but different side lengths, ended up with the same angles (plus/minus some drawing error).Then we use the trig tables (not calculators yet).Trig is easier for students after the discovery exercise.My entire knowledge base of real life examples (not the crap in the book) is always used in trig, geometry, algebra, calculus and applied calculus.People who insist on memorization, and/or students who prefer to memorize instead of think, are doing it wrong.Btw, military scopes are in radians.
Reply:
Originally Posted by n00b
[snip]... all problems u shouldn’t need to memorize anything, no formulas, nothing... just walk in with xtreme intuition.
Reply:High school geometry had very little to do with my machinist profession, when I did the geometry books in the apprenticeship, the very FIRST words in the book were"If you've had high school or college level geometry then you will be in trouble in these books". Well I had taken geometry and was totally lost & the geometry in the apprenticeship came easily to me because I actually had an application for using it, unlike the planar geometry from highschool.IMPEACH BIDEN!NRA LIFE MEMBERUNITWELD 175 AMP 3 IN1 DCMIDSTATES 300 AMP AC MACHINEGOD HELP AMERICA!Freedom is never more than one generation away from extinction.We didnt pass it to our children in the bloodstream".RONALD REAGAN
Reply:
Originally Posted by MinnesotaDave
My entire knowledge base of real life examples (not the crap in the book) is always used in trig, geometry, algebra, calculus and applied calculus.People who insist on memorization, and/or students who prefer to memorize instead of think, are doing it wrong.
Reply:Being a member of a minority should not excuse anyone from doing the job they are paid to do. He, and others I've known of since, use their minority status to protect them from consequences of not being professional.It should not mater what minority you belong to, The job you took, and are being trusted to perform should be done to the best of your abilities.An optimist is usually wrong, and when the unexpected happens is unprepared. A pessimist is usually right, when wrong, is delighted, and well prepared.
Reply:
Originally Posted by Willie B
Being a member of a minority should not excuse anyone from doing the job they are paid to do. He, and others I've known of since, use their minority status to protect them from consequences of not being professional.It should not mater what minority you belong to, The job you took, and are being trusted to perform should be done to the best of your abilities.
Reply:
Originally Posted by n00b
Well with school math books are filled with contradictions.Ie. In alg we state domain restrictions... yet in trig we dont as it gets too complicated. Also the more advanced the trig and stuff the less it intuitive it becomes. Do u know how to visualize what matrix division or Cramers rule or anything. No, because its too abstract and it is useless because it can be solved with systems or other things which are intuitive. Sure they make be useful and sometimes cool but they are unnecessary if they cannot be taught well enough to be completely intuitive.l I dont agree with memorization at all which is why all problems u shouldnt need to memorize anything, no formulas, nothing... just walk in with xtreme intuition. The reason y it isnt taught that well is b/c it takes enourmous skill and communication on the teachers part to break down these things intuitively, ez for them to just say memorize this or recite from the book.
Reply:
Originally Posted by MinnesotaDave
...Btw, military scopes are in radians.
Reply:
Originally Posted by MinnesotaDave
This is the most ridiculous thing you've said yet. It is likely the most ridiculous thing I've ever heard in regards to math.Since physics and chemistry are applied math, we shouldn't teach any math there either then. Just be "extremely intuitive." Absolutely ridiculous to the point of purposeful ignorance.I think maybe you should read up on this: https://en.wikipedia.org/wiki/Dunnin...3Kruger_effect
Reply:I gotta get me sum big werds. I'd b smart.An optimist is usually wrong, and when the unexpected happens is unprepared. A pessimist is usually right, when wrong, is delighted, and well prepared.
Reply:
Originally Posted by Willie B
I gotta get me sum big werds. I'd b smart.
Reply:Here's some geometry that's not well known. Gons
Reply:Just what kind of black magic are you up to, doug w?
Reply:
Originally Posted by n00b
Lol Dave. I checked out the Dunner Kruger affect. Good roast, but i have to say... I actually dont use physics formulas and so far i am doing ok in the class. I usually take the integral or derivative of the problem for visualization help as i just cant remeber those pesky formulas (really bad short term memory). Havent taken calc tho next year i think, so it was all self taught back in the day. Ive always have been passionate about math and science, which is why i stress extreme intuition because when it comes down to inventing the next formula like E=mc^2, stuff doesnt beat intuition and thought experiments at all. Keep in mind i tutored kids in math for money and i usually stress intuition as key! Sometimes my intuition is wrong, but it sure beats memorizing stuff. |
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发表于 2021-9-1 23:14:33