Help with geometry

[n00b]

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.

Ok man. Will do that. Cheers

[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.

[doug_w]

Here is the "finished" project for my class. Thanks again for the help. Went together pretty easy once I got going.

[MinnesotaDave]

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.

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.

[Virgil5]

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.

[William McCormick]

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.

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

[MinnesotaDave]

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

I use math when it's the proper tool for the job.

When other methods are more appropriate, I use them instead.

I find most people do the same if they have the math skills already.

When they don't have the math skills, they use other skills - perfectly normal in my opinion.

[Willie B]

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.

[Denis G]

Using a compass and a little math:
Hexagon inscribed in a circle:
https://www.mathopenref.com/constinhexagon.html
Slant height of a cone:
https://www.mathopenref.com/coneslantheight.html
Addendum: Truncated cone slant height:
https://math.tutorvista.com/geometry...of-a-cone.html

[n00b]

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.

Well with school math books are filled with contradictions.
Ie. In alg we state domain restrictions... yet in trig we don’t 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 Cramer’s rule or anything. No, because it’s 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. I don’t agree with memorization at all which is why all problems u shouldn’t need to memorize anything, no formulas, nothing... just walk in with xtreme intuition. The reason y it isn’t 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.

[MinnesotaDave]

[snip]... all problems u shouldn’t need to memorize anything, no formulas, nothing... just walk in with xtreme intuition.

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

[CAVEMANN]

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.

[OMB]

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.

It is people like you that are true teachers", many in the profession seem to be disconnected from their purpose and goal. There are some that simply aren't interested in what they are doing or believe a student is set for life with the group of memorized facts that they are filled with. I had a math teacher that was somewhat of a contradiction; he would present the concepts (trig I think) then apply to some real world uses but when asked by a student why we had to learn this, he replied "it is just good to know", as if we would never use calculus, trig, geometry, etc. A student is more likely to learn and retain if he thinks it has value.

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.

That is not a teacher or a person acting professionally, unfortunately there seem to be a few in every school and in today's society it is worse because they are protected by unions. It did seem way too many courses were memorize and recite for the sake of occupying the attention of kids, essentially as you say- babysitting. The result is- for example- an employee that I had that would mention daily he was a high school graduate but couldn't read a tape measure.

I had an English teacher like your math teacher. He would pick out 1 or 2 in the first week of the semester in each class to be the target of his abuse, destined to fail the class. I was marked with another and got an F. Failed the makeup course with him. Took the course in my senior year with a different teacher and got a C- IIRC. Since I struggled in "language arts", my parents thought I wasn't applying myself, I was somewhat vindicated when my mother told me a few years later that she learned the "educator" and school had been sued by a student 2 years behind me and won!

[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.

[OMB]

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.

Ironic you mention minorities... the laborer that couldn't read a tape did play the minority card on the way out, another guy corrected him and pointed out that if that was the case, he wouldn't not have had the job in the first place.

I'll take your last comment a step further; EVERYBODY should do their job to the best of their abilities. There is more honor in a trashman doing the best he can than a doctor doing just enough to 'slide by'.

[Insaneride]

Well with school math books are filled with contradictions.
Ie. In alg we state domain restrictions... yet in trig we don’t 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 Cramer’s rule or anything. No, because it’s 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 don’t agree with memorization at all which is why all problems u shouldn’t need to memorize anything, no formulas, nothing... just walk in with xtreme intuition. The reason y it isn’t 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.

Great minds think alike. To quote Albert Einstein " Never memorize something you can look up".

With the Internet and goooogle, everyone's a genius or a weldor.

[Insaneride]

...

Btw, military scopes are in radians.

If you ment rifle scopes, most if not all rifle scopes use radians. Some weapons use stadia or Kentucky windage to gauge distance of a Russian helicopter, Spetznaz or other object. The military does use alignment/measurement telescopes with gradients tho. Gradients makes the math easier for some because a circle is split into 400 instead of 360 or pi. Does that help you?

[n00b]

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

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.

[Willie B]

I gotta get me sum big werds. I'd b smart.

[Insaneride]

I gotta get me sum big werds. I'd b smart.

Here's one for ya: steradian

It's geometry or trig cone angle in 3 dimensions. It's used in micro scope telescope stuf.

[Insaneride]

Here's some geometry that's not well known. Gons

[TimmyTIG]

Just what kind of black magic are you up to, doug w?

[MinnesotaDave]

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.

You keep coming back to that, you do realize I don't advocate for memorization over thinking right?

Tutoring is fine and all, but it seems you missed the fact that many math "formulas" or processes become second nature over time.

Groups of them rattling around in your head become the foundation for math intuition.

Some people use formulas for as many things as they can, whether looked up or remembered. They aren't wrong.

Some people prefer to "play with a problem" and solve it however it occurs to them. They aren't wrong.

In my opinion, the only ones who are wrong are those who only want memorized process and formula. That approach is too limited for problems in actual career fields.

For the record, not only have I tutored for high school and college math, I've also tutored math for nurses, ultrasound physics, psychology, US constitution and sociology.
In my 11th year of teaching now and taught in county jail, alcohol/drug rehab, alternative schools, Indian reservations, and now in a traditional rural school (math through Calc and all shop classes).
I've taken students who are several years below grade level and caught them up to passing the MN state math test in only 2 years.

The one thread that ties them all together is "think, don't just do." Memorization can not accomplish what proper thinking can.

Also, I'm not an extremely intelligent man, I just work for how ever long it takes to understand.