Need Smart Person (math question)

OK, someone please help me! I need to know the diameter and area of a 36-sided polygon. Each side is of equal length, at 48 inches (for simplicity, 1.3m).

Please bear in mind that the Florida public school curriculum didn't include algebra30 years ago, much less trig or algorythm. So please speak to me as though you were speaking to a poor carpenter (because you are). As such, I can compute area, volume and surface of Cube shapes but this one is kicking my butt.

 

A regular 36-gon. connect each vertex with the center. Those 36 triangles have an anggle of 10 degrees.

OK. so we have 36 iscocolise triangles with an angel of 10deg and a base of 48in.
24/altitude=tan(5). so altitude=24/tan(5deg).
Area of each of those triangles=altitude*48=1/(2*tan(5))=5.715026151.

Area of 36-gon=36*5.715026151=205.7409414 square inches.

 

Woah I was coming here expecting something like "What is the square root of 49? OMG!!!"

I think MikeE helped you though ^_^

 

The area boils down to 864(24/tan 5°), which is 237,013.56 in².

The diameter (assuming you mean that between two opposite corners) boils down to 2(24/sin 5°), which is 550.74 in.



Longer story: A regular polygon of 36 sides of 48 inches can be divided into 36 isosceles triangles, each with a base of 48 inches.

Those triangles can be divided in half, giving you 72 right triangles with an angle of 5° and an opposite side of 24 inches.

24 divided by the tangent of 5° gives 274.32 in, the height of our triangles.

That times 24 gives 6583.71 in², double the area of one of the right triangles, or the area of one of the isosceles triangles.

That times 36 gives the area of all those isosceles triangles together, which is the total area of the polygon, 237,013.56 in².

 

Actually, Zoomie; I grew up in Florida, and attended public school there from 1959 through my high school graduation year in 1969; and the junior high school I attended in Fort Lauderdale, Florida had; as part of their required curriculum; Algebra I, Algebra II, and Geometry. Then, if one showed a propensity for mathematics by the end of the school year in Geometry, they were automatically registered for the following years; classes in Physics and Trigonometry. I did well in both Algebras I and II, but passed Geometry by the skin of my teeth; so I diverted down a different educational path at that point. In what town and what year did you attend public school in Florida? Judging from your comment, I guess the Florida school system experienced a decline in quality.

Regards, Michaela
____________________________________

"They will never make a perfect heart until they make one
that can't be broken."
....... The Wizard, "The Wizard of Oz"
____________________________________

 

Wow, I forgot about this thread... Thanks to all. This is for an off the grid yurthouse I'm designing for construction in WV starting next year. Now that I have the equations, I can adjust accordingly. Thanks much!

Michaela, I attended Howie Academy in Howie in the Hills from 1974 until 1977. Their curriculum was fairly rigorous but more centered on language arts. When I returned to public school in 1977, I basically slept for two years, dropped out at 16, took my GED, scored a 94% and then went back and told my priniciple at Rockedge High School his entire faculty were losers and were failing to do their jobs. I mean, they letme sleep through 4 periods each day and still gave me passing grades.

I was a pretty angry then. Looking back it was private school that put me ahead of the public school system. Eh, no regrets.

PS - none of the above mentioned math disciplines were required. Only basic mathematics.

 

well zoomie,, dont feel bad for needin assistance i was educated much later then you were and aint no way i could have figured that out.... then again i dont care for math either...... then again i didnt see her answer your question either...

 

More Math: The odds of needing to know this information in an average lifetime is 1 in 3,658,655,014.

 

my point exactly!..

 

(1) Peter Rabbit showed up at the Infinity Hotel one evening, but the clerk said it was full. Peter said the clerk could make room if he was willing to rearrange the guests. But how?
(2) Peter was impressed by the service, so the next night he came back with an infinite number of friends, but once again the hotel was full. How could the clerk accommodate all these new guests by rearranging room assignments?

 

Now here's a problem I would really like an easy answer to:
How can I post mathematical symbols on the Internet? I'm talking integrals, greek letters, infinity symbol, subscripts, superscripts, large and small case letters as per traditional printed math texts, you get the idea. What is the best freeware software package for doing this type of thing, and is documentation available so that someone can learn to use it?

 

Most word processors have the font, "Symbol", that has most of what you'll need.

Also check Mathgoodies.com: http://www.mathgoodies.com/forums/default.asp

And MathForum.org: http://mathforum.org/

And these might help: http://www.roie.org/work.htm and http://www.roie.org/acad.htm

Peace,
poor_old_dad

 

Ummm... He put on a Cho Sang Heui mask and shot all the guests?

I told you I'm no good at math...

 

The hotel clerk emptied the hotel. He put the new guest into room 1. Each other guest who had been in room 'n', he reassigned to room 'n+1'.

On the second night, when an infinite number of new guests arrived, the clerk emptied the hotel. He put all old guests into odd numbered rooms and all new guests into even numbered rooms.

 

Peter took a course called Logic 103. The one hour classes were held Monday to Friday each week for 12 weeks. On the first day, the professor said, "Some day this term, there will be a surprise examination worth 10 % of the grade."

Peter started frantically waving his hand until the professor called on him. "Sir, he said, it's impossible for you to give us a surprise exam!" He was correct, of course, but how did he justify his statement?

After he justified himself, the professor said, "You're going to die a surprise death some day." Once again Peter argued that this was impossible -- but how?

 

Obvious isnt it?

If I am 100% certain that today I may have an exam I will not be supprised either if it is true oir false that today an exam takes place. Similarly everyones death is a suprise yet everyone knoiws tjhey will die

 

Peter said,
"There are 57 days in the course (allowing for holidays). Let's suppose it's the last day, and the surprise exam hasn't been given yet. Since you, the professor, have said there will be a surprise exam during the term, it must then be given on the last day. This being the case, it wouldn't be a surprise. That rules out the 57th day.

"Now consider the 56th day, and assume the surprise exam hasn't been given yet. Then it must be given that day, since it must be given on some day, and since the 57th day has been ruled out. But then it can't be given on the 56th day, since it wouldn't be a surprise.

"Proceeding inductively, the surprise exam can't be given on any day this term, since given any day, 'n', if it hasn't been given on days 1, 2, ... n-1, and cannot be given on days n+1, n+2, ... 57, it can't be given on day 'n', since it wouldn't then be a surprise.

"Now let's take the question of my surprise death. For the sake of argument, let's define a 'day' as being a 24 hour period, measured from 00:00:00 (midnight) to 23:59:59 local time. We need to define the term surprise. Let's say that if I know for certain that I am going to die that day (as defined above), that death is not a surprise.

"Furthermore it is an empirical fact that humans do not live longer than 120 years, using the usual clocks based on solar synodic time. My date of birth is 16 June 1947. We can consider it a fact to say that I will be dead on or before 16 June 2067, midnight of that date local time. Again let us say that a death is not a surprise if I know in advance that I will die within the following 24 hour period.

"The use of the time interval, 24 hours, is arbitrary to the argument. Some time interval must be used in the definition of a surprise event. It could be one day, one minute, or one millisecond. The conclusion of the inductive argument still holds.

"So, let's assume I'm alive on 15 June 2067, my age being 119 years 364 days, but that no one lives to 120 years. Then I must die in the next 24 hours. Then my death in that day will not be a surprise, as defined above. That rules out a surprise death on 15 June 2067.

"Proceeding inductively, on 14 June, 13 June, 12 June 2067 and so forth, we can rule out days (or minutes, or milliseconds) consecutively as being candidates for a surprise death. Since the number of days from birth to death is a finite set, and since inductive proofs apply to finite sets as well as countably infinite sets, it follows that it is not possible for me to die a surprise death on any day, given the above definition of 'surprise'."

The professor of logic, finding himself checkmated by this argument, responded by going out and getting very, very drunk.

 

The way I heard that story was slightly different.

The prof didn't feel defeated. As a matter of fact, Peter (confident in his analysis) was surprised at the start of the next lecture when the prof handed out a test (worth 10%).

 

I suspect that the way out of this little mess is that surprise is not either non-existent or total. But there is a range of degrees of surprise, for example if an alien appeared now and gave me the meaning of life, i guess i'd be about as surprised as its possible to get. If a car crashed outside my window i'd be fairly surprised but less so than the alien. So for the case where the exam is on the last day it is indeed true that the test cannot be that day as there would be a 100% chance it is that day. However on the 56th day there is a 50% chance the test will be that day. A 33% chance its on the 55th day, so on and so forth. Therefore the real question is a what point do you consider it a surprise? If anything but total certainty is a surprise then it could be a surprise on the 56th day. Infact if you demand surprise to use the definition that its an event you have no reason to expect then total surprise is lost the minute that we are told that there will be a surprise test. From that moment it is possible to work the probability that your test will that day. The conscientious student of course may work out the probability and thus never be totally surprised using this definition.

The inductive proof is a very rigorous way of saying if you know it'll happen sometime then it can't be a surprise, common sense and inductive logic there in total agreement. This does of course mean that the surprise death puzzle of some meaning. If you have accepted your mortality then you can never be totally surprised by your death. Though this is more about the definition of surprise than logic.

 

It also shows that logic and its requisite tight definitions cannot completely describe the real world.

Just because we can explain some things, doesn't mean that everything can be explained. It doesn't mean we can't try though.