My kid brought some homework back and I sat down to help...... And got stuck *blush*
Well, his homework was easy, find the missing length or angle of a triangle etc. We finished that with no problems and I felt quite happy I seemed to of helped, but then he asked me about angles of a triangle -
Why are the angles always an exact figure, like 45 degrees or 61 degrees.
I should of just said, thats what the book says, but no, I went into explaining that the angles can have decimals and tried to explain about the Angle being built with Degrees and minutes / secs ... This sank in and then he said, -
What tangent should be used for a 32.47 degree angle ?
I grinned and opened the Trigonometric table page and found 32 degrees = 0.625
and 33 degrees = 0.649.. And said it lies within these too tangents.
But.... I couldn't explain what the exact tangent to use would be. I told him we'd revisit the problem and so here i am.... I've searched the net and havent found any such precise tangent tables or anything which will help me to understand and explain better the solution.
Sorry its a long one... Any help on this would be appreciated.
Whilst tiling the kitchen, I got to thininking about what shapes could be made with the tiles. in particular rectangles.
For example if I had 15 tiles, how many different arrangements of rectangles could I make. In this case it was two.
15 tiles = 2 arrangements 1 x 15 and 3 x 5
A stack of 1111 walls tiles ???
How many rectangular arrangements can be maded using 1111 tiles. Is there a formular for working this out ?
Ive searched for an answer on the net, but haven't found anything to help.
Any pointers would be great
You have probably all seen or read about Fermat receiving a letter asking if 100895598169 is prime and quickly replying that it was a factor of 112303 and 898423.
Anyway, I was trying to find out how he worked it out. Knowing the answers gives a huge help in finding a method, but don't think he did it the same way.
100895598169 X 8 = 807164785352
Sqrt of 807164785352 = 898423
100895598169 / 898423 = 112303
Can anyone come up with other methods ?