One of the actions is to find the points of intersection of a straight line with a circle. Here is a gif showing the result:
The algebra needed to solve the two simultaneous equations is straightforward, but a pain in the butt to get right and code up, so I thought “Why not solve the equations for the very simple case of the circle centered at the origin and the line vertical, at the same distance (a) from the centre of the circle
Then it is a simple matter of rotating the two points (a,b) and (a,-b) about the origin, through the angle made by the original line to the vertical, and then translating the circle back to its original position, the translated points are then the desired points of intersection.
The same routine can be used for the intersection of two circles, with a little bit of prior calculation.
Filed under geometry, math
Instructions: Read at least twice !
Originally posted on Mathemagical Site:
How do you measure a line?
In foot or meter, yard or rhyme?
Do rhythms or do logarithm
better keep your thoughts with them?
Could you draw figures of speech
if you had a compass and ruler in reach?
If armed with compass, quotes, and quips,
would you make an ellipsis or an ellipse?
View original 43 more words
CCSSM talks about “the standard algorithm” but doesn’t define it – Oh, how naughty, done on purpose I suspect, since there are varieties even of the “American Standard Algorithm”. Besides, if it is not defined it cannot be tested (one hopes!). I checked some internet teaching stuff on it, and as presented it won’t work on for example 403 – 227 without modification.
Anyway, I was thinking about subtraction the other day (really, have you nothing better to think about?), and concluded that subtraction is easiest if the first number ends in all 9’s or the second number ends in all 0’s. So, fix it then, I thought, change the problem, and here are the results
I am quite sure that some of you can extract the general rule in each case, and see that it works the same in all positions.
While I am going on about this I would like an answer to the following-
“If I understand subtraction, and can explain the ideas to another, and I learn the standard algorithm and how to apply it, and I have faith in it based on experience, WHY THE HELL DO I HAVE TO BE ABLE TO EXPLAIN IT?”
I guess this post counts as a rant!
I needed to move a point around a circle, in a computer graphics application, using the mouse pointer. It is clearly not sensible to have mouse pointer on the point all the time, so the problem was
“For a point anywhere, where is the point both on the circle and on the radial line?”
It may help to see the situation without the coordinate grid on show:
This is a problem with many ways to a solution, some of them incredibly messy !
For those of you who don’t know “Math with Bad Drawings” this is a real treat.
Originally posted on Math with Bad Drawings:
Our teacher’s gone utterly crazy.
No one can fathom her wrath.
She wants us to do the impossible:
She wants us to study for math.
How can you study for something
where talent is so black-and-white?
You get it, or don’t.
You’ll pass, or you won’t.
It’s pointless to put up a fight.
Her mind must have leaked out, like water,
and slipped down the drain of the bath.
I might as well “read up on breathing”
as study for something like math.
Math’s an implacable tyrant,
a game that I never can win.
And even if I stood a prayer of success,
how would I even begin?
My teacher, the madwoman, told me:
“First, list the things that you know.”
Her mind’s gone to rot.
Still, I’ll give it a shot,
though I’m sure that there’s nothing to—
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Thank you Audrey Watters for leading me to this exposure of the behaviour of testing corporations.
These two are MUST READs, and should be passed on to everybody:
I found this on http://www.playwithyourmath.com/ and adapted it a little.
The number 25 can be broken up in many ways, like 1+4+4+7+9
Let’s multiply the parts together, getting 504 (or something near)
Problem 1: Find the break-up which gives the max product of the parts. 1+1+1+…+1 is not much use.
Problem 2: Find a rule for doing this for any whole number.
Problem 3: Put this rule in the form of a computer algorithm (pseudocode is OK)
Problem 4: Write the rule as a single calculation (formula)
I found this on Quora. What would the standard algorithm be, I wonder.
Suppose you have five loaves of bread and you want to divide them evenly among seven people. You could cut the five loaves in thirds, then you’d have 15 thirds. Give two of them to each of the seven people. You’ll have one third of a loaf left. Cut it into seven equal slices and give one to each person.
There may be other solutions. a = b = 3, c = 21. (Egyptian Fractions)
Mary’s mother brought a pizza
For her little kiddies, two.
“Johnny, you can have threequarters.
Mary, just a half will do.”.
Then the kiddies started eating.
Soon Mary grabbed her final piece.
“That’s mine” screamed Johnny, then the fighting
Broke the tranquil mealtime peace.
How much pizza then was eaten?
How much pizza on the floor?
Mother swore and left the building.
“I should have ordered just one more”.
“How’s your Mary doing?”.
“She’s doing well. She’s 8 now. She’s in Grade 3. She really enjoys the Pre-Algebra and the Pre-Textual Analysis.”.