Prove 1 = 2

mathxyz · 2024-05-08 10:40:41

Watch this clip and tell you what you think.

https://m.youtube.com/watch?v=hI9CaQD7P6I&pp=ygULUHJvdmUgMSA9IDI%3D

Keep_Relentless · 2024-05-09 01:03:45

These "proofs" typically rely on a division by zero.

mathxyz · 2024-05-09 08:03:39

Keep_Relentless wrote:

These "proofs" typically rely on a division by zero.

What's your point here?

Phrzby Phil · 2024-05-09 09:21:31

The point is that there is most likely a division which is not obviously by zero, but close analysis shows that it is, and yet the subsequent lines rely on the quotient being a real number.

mathxyz · 2024-05-09 09:52:12

Phrzby Phil wrote:

The point is that there is most likely a division which is not obviously by zero, but close analysis shows that it is, and yet the subsequent lines rely on the quotient being a real number.

Copy. Ok.

Phrzby Phil · 2024-05-09 12:06:03

Have you found which line has the division by zero?

mathxyz · 2024-05-10 07:27:59

Phrzby Phil wrote:

Have you found which line has the division by zero?

Show what you mean.

Phrzby Phil · 2024-05-10 10:40:31

Follow each line of the "proof." When you get to a division line, evaluate the divisor. If it = zero, then the following lines of the "proof" are invalid if they assume that the quotient is a real number, as opposed to the division being undefined.

mathxyz · 2024-05-10 23:49:26

Phrzby Phil wrote:

Follow each line of the "proof." When you get to a division line, evaluate the divisor. If it = zero, then the following lines of the "proof" are invalid if they assume that the quotient is a real number, as opposed to the division being undefined.

I will play with this one some more.

Bob · 2024-05-11 00:57:35

In the video I watched one of the students spots the fallacy towards the end of the clip. I wonder if the prof. knew he was being filmed. It looks like this was from a student's phone.

Bob

mathxyz · 2024-05-11 04:47:22

Bob wrote:

In the video I watched one of the students spots the fallacy towards the end of the clip. I wonder if the prof. knew he was being filmed. It looks like this was from a student's phone.
Bob

Wow! How embarrassing it must have been for the teacher. I think the clip shows a middle school class. Why on earth is a middle school math teacher teaching proofs to students between the age of 12 and 13?

Bob · 2024-05-11 05:06:23

I don't find it odd. I used to do a series of lessons on the nature of proof to 14 year olds. I might even have (but didn't) used that fallacy to show how careful you have to be when trying to prove things. My lesson had a 'proof' of Pythag by shuffling areas. I then followed it with a trick involving chopping a square into four with the challenge 'make a rectangle out of the bits'. The reason it's a trick I'll save in case you want to give it a try.

Bob

mathxyz · 2024-05-11 05:10:12

Bob wrote:

I don't find it odd. I used to do a series of lessons on the nature of proof to 14 year olds. I might even have (but didn't) used that fallacy to show how careful you have to be when trying to prove things. My lesson had a 'proof' of Pythag by shuffling areas. I then followed it with a trick involving chopping a square into four with the challenge 'make a rectangle out of the bits'. The reason it's a trick I'll save in case you want to give it a try.
Bob

Can you show the proof of the Pythagorean Theorem?

Bob · 2024-05-11 05:12:25

Yes but I am running out of time now and I've got a stack of replies to construct. I'll come back to these later.

Bob

mathxyz · 2024-05-11 05:19:04

Bob wrote:

Yes but I am running out of time now and I've got a stack of replies to construct. I'll come back to these later.
Bob

Thanks. No rush at all. We are having with mathematics.

Bob · 2024-05-11 06:03:55

Proof of Pythagoras Theorem.

Start with any right angled triangle. Make three more copies. Arrange them in two ways as shown in the diagram.

Does this prove that area A + area B = area C ?

Now get some paper (with squares if possible). Draw this shape. In my diagram the squares are 1cm by 1cm but it'll work ok in inches too. Draw lines as indicated and cut out the four shapes; two triangles and two quadrilaterals.

Try to rearrange the four shapes to make a rectangle.

Report back the length and width of your rectangle.

Bob

mathxyz · 2024-05-11 08:15:18

Bob wrote:

Proof of Pythagoras Theorem.
Start with any right angled triangle. Make three more copies. Arrange them in two ways as shown in the diagram.
https://i.imgur.com/qqvbgdh.gif
Does this prove that area A + area B = area C ?
Now get some paper (with squares if possible). Draw this shape. In my diagram the squares are 1cm by 1cm but it'll work ok in inches too. Draw lines as indicated and cut out the four shapes; two triangles and two quadrilaterals.
https://i.imgur.com/EgsLUwX.gif
Try to rearrange the four shapes to make a rectangle.
Report back the length and width of your rectangle.
Bob

Awesome!

Math Is Fun Forum

#1 2024-05-08 10:40:41

Prove 1 = 2

#2 2024-05-09 01:03:45

Re: Prove 1 = 2

#3 2024-05-09 08:03:39

Re: Prove 1 = 2

#4 2024-05-09 09:21:31

Re: Prove 1 = 2

#5 2024-05-09 09:52:12

Re: Prove 1 = 2

#6 2024-05-09 12:06:03

Re: Prove 1 = 2

#7 2024-05-10 07:27:59

Re: Prove 1 = 2

#8 2024-05-10 10:40:31

Re: Prove 1 = 2

#9 2024-05-10 23:49:26

Re: Prove 1 = 2

#10 2024-05-11 00:57:35

Re: Prove 1 = 2

#11 2024-05-11 04:47:22

Re: Prove 1 = 2

#12 2024-05-11 05:06:23

Re: Prove 1 = 2

#13 2024-05-11 05:10:12

Re: Prove 1 = 2

#14 2024-05-11 05:12:25

Re: Prove 1 = 2

#15 2024-05-11 05:19:04

Re: Prove 1 = 2

#16 2024-05-11 06:03:55

Re: Prove 1 = 2

#17 2024-05-11 08:15:18

Re: Prove 1 = 2

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