Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Several Question Experiments
Replies: 8   Last Post: Nov 19, 2013 5:38 PM

 Messages: [ Previous | Next ]
 David Elkins Posts: 17 Registered: 11/16/13
Re: Several Question Experiments
Posted: Nov 19, 2013 5:38 PM

On Saturday, November 16, 2013 4:09:40 PM UTC-8, Barry Schwarz wrote:
> On Sat, 16 Nov 2013 14:06:55 -0800 (PST), David Elkins
>
> <davidelkins777@gmail.com> wrote:
>
>
>

> >Question Experiment 1:
>
> >
>
> >Imagine a line infinitely long in both directions. Take a pair of scissors, cut it and push the two sections apart one foot. Insert a foot long line. Is the line now one foot longer than infinity?
>
>
>
> Draw line segment 1 from (0,0) to (2,0).
>
> Draw line segment 2 from (0,1) to (1,1).
>
>
>
> Drop any number of vertical line segments from segment 2 down to
>
> segment 1. Each point on segment 2 has a corresponding point on
>
> segment; they both have the same x coordinate. No point past (1,0) on
>
> segment 1 corresponds to any point on segment 2. So segment 1 has
>
> more points than segment 2.
>
>
>
> From point (0,2), draw any number of line segments to points on
>
> segment 1. Each drawn segment passes through segment 2. Each point
>
> on segment 1 has a corresponding point on segment 2 and each point on
>
> segment 2 has a corresponding point of segment 1; the segment 1 x
>
> coordinate is twice the value of the segment 1 x coordinate. So
>
> segment 1 and segment 2 have the same number of points.
>
>
>
> Once you understand how both conclusions can be correct, you will have
>
>
>
>
> <snip>
>
>
>

> >My name is David Elkins. I came up with these two questions and would like to know what people think of them.
>
>
>
> The first has been a standard discussion item in mathematics courses
>
> for at least 6 decades and probably very much longer.
>
>
>
> --
>
> Remove del for email

Hello, I posted the initial thread. I have been unable to get to the Google groups for the last few days. I will take the next day or so looking at the various responses. I will do my best to get a 'content' reply to each. Sorry about the delay. Thank you, David,

Date Subject Author
11/16/13 David Elkins
11/16/13 Michael F. Stemper
11/16/13 David Elkins
11/17/13 Peter Percival
11/18/13 Michael F. Stemper
11/16/13 Barry Schwarz
11/19/13 David Elkins
11/17/13 Tucsondrew@me.com
11/17/13 ross.finlayson@gmail.com