A little problem. How to calculate the length of one side of a scalene triangle without using cosine formula, which is what I think your comment refers to.
Here's the triangle. If it's not what you need or think is useful, you've exhausted my ingenuity (and my memory) :)
Angles at A and C are 55 and 40 degrees respectively. (Someone might want to do the sums, I just measured mine with my wee draughting table and it looks about right.
OK. The length of AB is 5 units, the length of AC is 8 units, crucially the height HB is 4 units. (Looking familiar?) HB forms a right angle with AC.
The unknown quantity is BC.
To calculate:
AB squared is the sum of AH squared + HB squared ie 25 (5) = 16 (4) + 9 (3) AH = 3
Therefore HC = 5 (8 - 3)
HC squared = 25 + HB squared = 16 gives us BC as the square root of 41, about 6.4, give or take.
Of course this all changes when we start to accelerate towards the speed of light and all those nasty Lorentz contractions start messing up the arithmatic. So whatever you do, don't under any circumstances try and teach this to tachions. It also breaks down a bit at the Planck length, but doesn't everything? Including me?
The unknown quantity is BC.
To calculate:
AB squared is the sum of AH squared + HB squared ie 25 (5) = 16 (4) + 9 (3) AH = 3
Therefore HC = 5 (8 - 3)
HC squared = 25 + HB squared = 16 gives us BC as the square root of 41, about 6.4, give or take.
Of course this all changes when we start to accelerate towards the speed of light and all those nasty Lorentz contractions start messing up the arithmatic. So whatever you do, don't under any circumstances try and teach this to tachions. It also breaks down a bit at the Planck length, but doesn't everything? Including me?
Hmm. Let me see if this will work. So, assuming we know to advance from C left 9 units, we then angle our cursor at B 55 degrees and then travel north 5 units.
ReplyDeleteWe then do not yet know the angle that B is going to be. That is part of the problem. We have a cursor dangling at B pointed toward C, but we don't know how many units it is to C and we don't know the precise angle since the angle of C is not yet formed, nor will it be formed until we get to C.
Now, we DO know that it will be a number between the difference of 180 and 55, and 90 because all triangles equal 180 degrees. And from looking at it, we can discern that it will be the larger of the two angles, and that it is larger than a 90 degree angle. We also know that no two angles of an obtuse are the same; but other than guessing, we can't really tell our cursor (unless I miss something here) what degrees to make B, because we don't know the precise angle of C.
What I want to do, and I know there must be some mathematical way to do it though I'm not smart enough yet, is to decipher the two angles from the information of the length of two sides and a single angle. Normally, that would require Trig functions, which our students are not yet ready to do. I believe there exists a simpler formula, one which I have in my forest of thought, overlooked.
So, since you brought up imaginary side BH, I think maybe that is the way to do it. BH will form a right angle to AH which we then know is a 90 degree angle. And AH is 55 degrees. So that makes BH 35 degrees.
But how do I tell if I've split the angle right down the center? In fact. I know I haven't because angle BC is much larger than 70 degrees. So, I'm right back where I started.
I really don't see how to do this without trig functions, but I do hope to find a way.
OK, start at (c), draw an 'infinite' line at 35 degrees, go back to (c) go horizontal for 9 units, stop, draw an infinite line upwards (from (a)) at 55 degs, where the lines intersect is (b) no angle at (B) is required. It makes itself. Once you transect the angle b to h the two triangles provide their own solutions to the angle problem. QED!
ReplyDelete35 should be 40 in the preceding comment, I forgot I changed it :)
ReplyDeleteJees, one day I will get round the numbers! And draw accurately. The baseline a to c is 8 units not 9, even this dumb Klutz knows that the square root of 52 has to be greater than 7. So
ReplyDeleteRevised post now posted.
So, if it is all right with you, I'm going to take this to work tomorrow and try it out on Turtle Logos. If it works, I will let you know.
ReplyDeleteOtherwise, you stay in the doghouse. ;)
Just kidding.
Define: Capricious
Capricious?
ReplyDeleteRelating to caprice, a chronic and recurring condition caused by a surfeit of oestrogen.
Strangely, the carriers themselves show no signs of illness but those around them display all of the signs of insanity; drooling, head banging, screaming, incoherent babbling.
These symptoms are best dealt with using copious quantities of alcohol liberally applied to the inside of the stomach.
From the Italian musical direction, 'capriccioso'; 'lively','free'.
Uhm. I'm incorrigable.
ReplyDeleteJust get on with the QED.
I'll blog you from the inside of the mental ward, if need be.
So, In the end, the "Go home" command is the only other way to do it correctly, other than trial and error or using a ratio between the length and the degrees (which is sins and cosins, correct?)
ReplyDeleteSeriously, we can progress to QED. I'm going to have to do a little catch up on the maths and formulas.
Speaking of, what is your favorite way to memorize a formula?
Flash cards?
Writing it?
Singing it?
Leave an answer where I'll find it. :)
The American
I amblogging you from the inside of a mental ward...........
ReplyDeleteYou have my word, capricious though it is....
ReplyDelete"The Boy in the Striped Pyjamas" finally hit here this week in a big way, which I believed you mentioned a while back.
ReplyDeleteOne review mentions Primo Levi's "If this is a Man."
Do you have it?
I think I will watch the film to inspire me to forge ahead.
If you have the Primo Book, and the time, perhaps you can do a quick scan for any possible inspiration.
I will (from inside my cage) let you know specifically what I need help with if you are willing.
As always, I thank you for your time and attention.
The faerie
Yes and I re-read it every few years (I'm now on my third copy, paperbacks are too flimsy but hardbacks are too expensive in the short term) just so that I, at least, do not forget.
ReplyDeleteIt is, as all Levi's work is, beautifully written but the beauty of the prose in no way diminishes the horror, merely enhances it, makes it worse.
It is not a book to read on the tube/subway to work unless you can steel yourself. Too often one finds small drops of water making round spreading stains on your green shirt :) and they show!
I cannot think of any other book I would recommend above all others for an 'appreciation' not a scholastic description of the holocaust.
"We fought with all our strength to prevent the arrival of winter.......We know what it means because we were here last winter; and the others will soon learn. It means that in the course of these months, from October to April, seven out of ten of us will die. Whoever does not die will suffer minute by minute, all day, every day:....."
To be ABLE to write this, to reconjure the memories that should be kept hidden, buried, for the sake of one's own sanity; this, I think, is inspirational enough for all
I don't understand your comment but I assume it is part of a plea for your friend.
ReplyDeleteI do understand why women stay, but there are no good excuses and because of their illusions (which act as a drug to impede rational thought) it is up to us, their friends, to plead with them for their own safety, to speak out and stand up for them when they cannot stand up for themselves.
Sadly, I have known several abused women and what I know is that they gravitate toward abusers, even after the relationship ends.
That is why I insist on a "fierce recovery."
You will see in further posts just what I mean.
I've come to the epiphany that you need to start a website called
ReplyDeleteEncyclopaediaMan.com. You can charge 1 pound (or whatever the equivalency is of a US dollar) per minute.
You can also have loads of fun twisting people's brains into pretzels. :)
I already have a moniker (other than 'bastard!'), it's Pipe Cleaner Man! It's what I'm made out of :)
ReplyDeleteStop calling yourself names. You are a talented man who has not realized his dream.
ReplyDeletePast failures are small excuses. Make an exciting life for yourself however you can.
Please.