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#1 Re: Help Me ! » Radius » 2017-11-04 23:05:04

Hi Animesh,

Join R to the centre, O, of the circle. Triangles OPR and OQR are congruent as they have a 90 degree angle and one side in common plus equal radii, OP and OQ.

So OR is a line of symmetry .  If OR crosses PQ at S then SP = 3,so RS = 4 by Pythagoras.  If you let OS = x and radius = r you can form two equations in r and x by Pythagoras on OPR and on OPS.

It's easier to eliminate r and find x.  Then find r.


#2 Re: Help Me ! » Geometry help! » 2017-11-03 23:14:24

Hi sydbernard,

I'm hoping I've understood this.  I'm slightly worried by the term disc rather than circle.

Let''s say the disc has radius r and the required circle has radius s.  The centre of the disc is O, and the line halfway between the parallels is m.

With centre O and radius r + s an arc cutting m at P will give the required circle centre.  So how to 'construct' r + s ?

If m cuts the disc at A, make a line perpendicular to m cutting one parallel at B.  AB = s. Extend OA and with centre A and radius AB make an arc to cut OA produced at C. Note: OC = r + s. With centre O and radius OC make an arc to cut m at P  P Is the required centre .

But what if the disc is too small to be cut by m ?

In that case you can draw a line n, perpendicular to m, through O. Let n cut the disc at E. Also draw any other line, FG, , parallel to n, so that F is on m and G on the parallel. FG = s.

Join F to E and construct GH parallel to FE with H on n. OE + EH = r + s so once again we have the right radius for an arc to cut m.


#3 Re: Help Me ! » Represent sqrt{2}+sqrt{3} on a number line » 2017-11-01 22:55:10

But what does 'exact' mean?  If you draw a line 1 inch (or cm) long is that exact?  Suppose you look at the line through a magnifying glass.  How do you know it is not actually 0.99999 ?  I think you are creating an unnecessary difficulty.


#4 Re: Help Me ! » Can someone please help me with this: 2x + 4cosx = 0 » 2017-11-01 00:48:23


There isn't an exact value for this so you'll have to give an approximate value.  On the MathsIsFun main site there is a function plotter.  You can plot -x as one line and 2cosx as a curve.  Zoom in to get your answer where they cross.

#5 Re: Help Me ! » Represent sqrt{2}+sqrt{3} on a number line » 2017-11-01 00:40:41

Hi Abbas 0000

What are you accepting as a 'representation'?  If you draw a line and Mark points at regular intervals, labelling them 1, 2, 3, etc you have to assume you can do that accurately.  In Euclidean geometry we assume you can, but in the real world there is no such thing as perfect accuracy. Pencil drawn points have size and, by viewing under magnification, you will reveal that drawings are never exact.

So I think what you have described is acceptable.  Draw a unit line from zero to point A and then a vertical line up of one unit to point B.  With compass point at zero and radius OB make an arc to cut the number line at C.  OC is root 2.

This point is as accurate as A, so if the point for 1 is acceptable so is C.

Draw a line vertically up from C one unit, to point D. Compass set to radius OD and make an arc to cut the number line at E. This is root 3.

Repeat the root 2 construction from point E and F will be at root 2 + root 3.


#6 Re: Help Me ! » Sangaku Problem 525 » 2017-10-30 23:37:19

EOdash = r2

AOdash = d - r2

KJ = r3

AJ = 2r1 - r3


#7 Re: Help Me ! » what is Brute-force search in numerical analysis, » 2017-10-29 18:52:06

Say you have an equation in n, where n is a positive integer less than 10000.

A brute force method would be to try every possible value for n, and see which values work.


#8 Re: Help Me ! » Geometry help » 2017-10-29 18:49:12

Again no diagram for the first three.

You have correctly found the angle sum for the polygons. In a regular polygon all the angles will be equal, so now calculate one of them.

Your scale factor is correct for small shape as a fraction of the large shape.  I think the second answer is for large as a multiple of the small.

In the last a minus sign is needed.  I'm not seeing that.

What course are you studying?


#9 Re: Help Me ! » Geometry work need help! » 2017-10-29 18:41:44

I don't think it is possible to help without a diagram.  Sorry.


#10 Re: Help Me ! » Fraction » 2017-10-29 01:00:12

Hi Animesh,

Write 1000n/810 = d25.d25d25d.......

Subtracting gives 999n/810 = d25

This will greatly simplify and you'll find only one value of d is possible.  The value of n follows easily from this


#11 Re: Puzzles and Games » The Professor and the Student » 2013-12-16 20:47:40

I thought this was totally sorted by Bob Bundy.  Maybe he wasn’t clear enough so I’ll have a go for him.

Let’s call the test availability period,  TAP, measured in days. 

The professor has declared:  Statement   = “…but you won't know in advance which”

So on Sunday evening,


As we reach the evening of each day without a test,  TAP reduces by 1 and if we count back one day TAP increases by 1.

Deduction one:  So by Thursday evening

   and so the student deduces that the statement implies  the test cannot take place on Friday, so

So far, so good.  But then the student’s logic goes wrong.  The student’s logic, not the professor’s.  Which is at it should be; he is the professor after all.  :)

On Wednesday evening

  .  But the student thinks
  because of deduction one and counting back one day.   And hence the test cannot take place on Wednesday, making

But  you cannot use deduction one on Wednesday evening , because deduction one requires that it is Thursday evening  and it isn’t.  You cannot use logic like this.

In post 56 Bob set up a parallel situation involving his next post.  In post 65 he made this post.  No one successfully predicted when he would post, but the post occurred.  He clearly wasn’t lying!

He also said he was giving up on the thread thereafter.  That’s why he has asked me to remind everyone about what he said; so he can maintain the position that he was not lying.  

I am, of course, happy to assist him.  smile

Alter ego

#12 Re: Puzzles and Games » The Professor and the Student » 2013-05-04 05:51:35

Agnishom wrote:

Ai do not mean to be rude, but I doubt your identity…

What do you mean?  I am who I am.  I recommend you re-read posts 57 and 66.


#14 Help Me ! » what does this become? » 2012-12-15 09:59:59

alter ego
Replies: 1

Can somebody help me do


#15 Re: Puzzles and Games » The Professor and the Student » 2012-03-30 09:34:33

hi guys,

You seem to be missing something.

In post 57 bob said he would post during the week but you wouldn't know when.

In post 66 he posted.  It was a Tuesday.  Nobody predicted that.

He also said "So, I'll have one last go and then I'm giving up on this thread."

So he is clearly not going to come back to this thread again.

Case closed.

alter ego

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