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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#26 Re: Help Me ! » Data Analysis - Statistics! » 2006-05-10 00:36:20

The first thing I notice is the link between pay scale and days absent. There pay scale is inversly porportional to the days they are absent. Employee I just needs the sack by the looks of things.

Is this a real company or a hypothetical maths question?

#27 Re: Help Me ! » Data Analysis - Statistics! » 2006-05-10 00:32:21

I think some of the data from the table is missing, or I'm not reading it right.

EDIT: Oh I see now.

#28 Re: Help Me ! » Math class is boring!!! » 2006-05-10 00:07:12

I love maths class. It's the only time I cam work on honing this equation for PI without geting in trouble. He he. And the work is so easy, there just something about being the only one in your class getting the right answer that makes you feel empowered.

#29 Re: Help Me ! » I Hard Question I Got In Maths!!! Need a Quick Answer » 2006-05-09 22:18:57

The roots of the parabola must be -35 and 35 if the y axis is the axis of symetry.

b must equal Zero because the parabola is not shifted left or right. So that leaves us with the equation:

c is 185 because when an x value of 0 is subbed and a y value of 185 is subbed in c is denoted to be 185.

That leave us to find a.

Sub in 35, 0 zero for x and y values respectively and you will find a = -185/1225. Leaving us with the equation:

And it seems to work fin when I sub values in I havn't looked into simplifying it.

(Hurray I answered my first "Help Me!" on the forum tongue)

#30 Re: Help Me ! » a°= 1 explain.. » 2006-05-09 21:47:39

Wow, I never knew exactly why that was until, i just accepted it, just like the idea that the moon is made of cheese and if you can yell loud enough ,the man in the moon will talk back.

#31 Re: This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-09 19:39:10

Hmm, but I need to know PI in order to mirror the graph .... grrr.

#32 Re: This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-09 19:14:13

I was graphing:

To show the degree of error. I don't know why I couldn't visualise it. But the graph was the same as:

But with an asimtope of y cannot = PI. I don't know how to express that in the line equation, nor does my teacher no the name of the kind of line in that equation. We just call it the side-ways half parabola.

I though perhaps If we could mirror this line [vertically] and average the y values of the two lines it would gives us the exact value of PI. Because the average of the mirrored lines would then become the exact value the lines cannot be.

(BTW, Who designed the (math)(/math) bbc code? I've never seen it on another forum before.)

#33 Re: Introductions » Mad Math! » 2006-05-08 20:02:16

Sounds like me if i was 11 years older, I have HSC next year and I better buckle down or I know I will really regret it.

#34 Re: This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-08 18:47:09

After reading up on it more I think I'm misunderstanding how it works ...

#35 Re: This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-08 18:38:16

These methods that involve creating more accurate representation of PI by increasing the number of time the SUM is repeated is impractical for calculating PI.

I've being looking at other methods, and there are algorithms that work by getting the n'th decimal of PI. Ie; Instead of increasing the accuracy each loop of the sum, it adds the next decimal place on.

Heres an example: http://fabrice.bellard.free.fr/pi/

I'm hoping to get the algorithm to work correctly in the computer program, then add functionality to check for redundancies and pattern. I'm not looking for the final repeating numbers and get the exact value of PI. I was thinking that perhaps there are patters. For example, any decimal place number which is a divisible of 'x' will always be 'y'.

#36 Re: This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-07 19:00:07

I came to this same conclusion over the weekend when I was reading more into radians. At first I thought that it would innacurate because radians were based around PI. The I realised that it wasn't based around the innacurate decimal PI but around an accurate constant PI. So the equation could be rearranged to generate an accurate representation of PI. I also found I get more accurate answers for questions using PI when i use this equation as PI is only accurate to 10 decimal places in my calculator, but I get many more ghosed decimals when I use this formula.

I'm currently working on a program to produce PI to many many decimals based on the forula, but I'm having trouble with with the Series for finding ArcSine.

Anyone experienced with C++?

#37 Re: This is Cool » Infinity » 2006-05-05 00:29:34

An English lesson, that's infinity isn't it?

∞ = 1/0

Try to split 1 evenly between zero groups. That would be infinity. Atleast based on the elemntary school idea that divsion is giving an equal share of x to y amount of groups.

#38 Re: This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-04 23:34:10

So the new formula would be:

(180/θ)√(2(1 - √(1-θ²))) ?

#39 Re: This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-04 17:34:14

Unless theres another way find the side of a non-right angle triangle when given 2 sides and the angle between them, I don't know any way to get rid of cos. And a radian incorporates PI, wouldn't that make my formula infinitly long? Since 180 = PI Radians? Or is that only needed when converting radians and degrees.

I'm doing year 11 Extension 1 maths. I'm not sure what the equivilent is in america, but were covering interiro and exterior reatios of line intervals. We just finished 3d trigonometry (which was so easy, its just 2d trig with more than one triangle, I found it especially fun because everyone else found it difficult lol). I just started thinking, "I wonder how they figured out was PI was?" when I was supposed to be studying, so I spent the next hour devising this formula lol.

I'm going to make a console app in C++ to print the value of PI according to the formula for as many as possible, but I'll have to settle using 10^-999 until I can find infinity, I guess thats just for a later formula lol. (Anyone know how to grab the first decimal place of a number?)

By the way Admin, I love the quote in your sig, it's funny because it's true.

#40 This is Cool » The Exact Value of PI. Well, not exactly ... » 2006-05-03 18:03:49

Zmurf
Replies: 27

Ok this is my formula for finding PI. If anyone can work out a way to present infinity as a number (lol?) then hurray! It's pretty stupid but here it is, my formula for finding PI.
                    ____________
PI = (180/θ)√(2(1 - COS θ))

The smaller θ is the more accurate PI will be found. So to find PI θ = 10^-∞. lol.

BUT when I was messing around on my calculator subbing in increasingly (or decreasingly) smaller numbers PI became for innacurate (in comparison to the first 20 decimal places of PI from google). But from my logic of the way i figured it out, a smaller number should yield more accurate representation of PI!

I did this. Break a circle into 4 RH Triangles. Find the hypotinuse (Spelling?) of all of them. You'll get a super innacurate measurement of PI. But it's split the circle into 4 90 degree segments. Using pythagorisis (Ok just overlook my spelling from here on out >.<) theorom c^2 = a^2 + b^2, the circumfrance^2 would be equal to (360/θ)*(b^2 + c^2) (θ being 90, to yield the 4 segments to multiply by th a^2 b^2 part of pythagorisis' theorum to get 4 times th elength of 4 congruentr triangles that made up my super rough circle) b and c would both be equal to the radius. But to make it more accurate I split the circle into more than 4 segments. segments of say 0.01 degrees each. but i can't use a^2 + b^2 to find the hypotinuse so I use extended pythag's theorum a^2 + b^2 - 2ab COS θ) since a = b i get 2r^2 - 2r^2Cos θ. whe nthe radius of the circle is 1/2 then the circumfrance is = to pi. which is why it is 180/θ not 360/θ so i wouldn't have to put the whole thing over 2. in pythag's theum the r^2 is consistent so it gets removed making it just r * √ which is how 360 gets halved. i lost the working out, now i forget how im getting places. you people are much better at this than me so i'm sure you'd understand, though my grammar drags, my grammar should be better since i'm in year 11 now ... anyways, yea thats pi .. still can't work out why a smaller number won't make it more accurate, anyone know?

#41 Dark Discussions at Cafe Infinity » Anyone Read 'Space' by Stephan Baxter? » 2006-05-03 17:45:55

Zmurf
Replies: 3

Halfway through this book and I must say ... WOW! For anyone who loves fiction, and loves astronomy and cosmology, this is the ultimate book. It ties real theories into and epic sci-fi novel. Anyone else read it?

#42 Re: Help Me ! » Number Systems » 2006-02-12 21:12:40

wots the difference between base 2 and base -2, bar the 1*(02)^1 its identical because 1*(-2)^2 = 4 just like 1*(2)^2, is there sumthin' im missing?

#43 Re: Help Me ! » Number Systems » 2006-02-12 20:09:43

Ricky wrote:

(Whoever thought up binary and applied it to computers was a genius...)

It came naturally because transistors only have two states.

But by far, the coolest base is -2:

0110 0110: 34 or 1*(-2)^1 + 1*(-2)^2 + 1*(-2)^5 + 1*(-2)^6

its not about transistors, its about charge in magnetic tape, there millions of seperate magnetic bits on a tape and the point either north or south, north being 0 south being 1. And its read by the computer.

#44 Help Me ! » Non-Linear Simultaneous Equations » 2006-02-12 19:54:05

Zmurf
Replies: 1

I need some help with Non-Linear Simultaneous Equations. Does anyone know of any good tutorial sites?

Also, will Cramer's Rule still work with NLSE? I don't see how it would with the addition of Greater Powers and Divisions.

#45 Re: Help Me ! » Has anyone seen this formula before? » 2005-08-01 09:37:03

MathsIsFun wrote:

Can I have a go at simplifying?

Start      : a² = (b sin Θ)² + (c – b cos Θ)²
Expand  : a² = b² (sin Θ)² + c² – 2bc (cos Θ) + b² (cos Θ)²
Combine: a² = b² [(sin Θ)²+(cos Θ)²] + c² – 2bc (cos Θ)

Now (sin Θ)²+(cos Θ)² = 1 (a Pythagorean Identity), so:

Finally: a² = b² + c² – 2bc (cos Θ)

(Well done recognising that formula, ganesh)

How did you get to the c² - 2bc (cos θ) + b² (cos θ)² ?

#47 Re: Puzzles and Games » Trains » 2005-07-31 22:36:40

if theres only one set of track incircling the town, how did they get one train to go one direction and one the other one. even if they were running at different times, if theres only one set of tracks then theres no where for the inactive train to wait.

#48 Re: Help Me ! » Has anyone seen this formula before? » 2005-07-31 22:32:36

Oh ok. But what formula would I use if i want to find the angle oposite to side 'b' if i'm only given the lengths of sides 'a' and 'b' and the angle between them?

#49 Help Me ! » Has anyone seen this formula before? » 2005-07-31 21:29:47

Zmurf
Replies: 11

Has anyone seen this formula before? Or one very similar?

a^2 = (b sin Θ)^2 + (c – b cos Θ)^2

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