Happy New Year, wherever you are!

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John Hanna

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Dec 31, 2024, 6:15:57 PM12/31/24
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Found the attached problem via Google News today and had nothing better to do!

 

Happy New Year!

Regards,

     John

 

Oxford Geometry Problem.tns

Travis Bower

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Jan 1, 2025, 1:00:55 AMJan 1
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fyi, typo page 1.3
Can you spot it?


Travis Bower, M.A.
Math Teacher
Dos Pueblos High School
tbower@sbunified.org
www.dphs.org
www.sbunified.org
805.968.2541 x4538

 


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Stephen Arnold

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Jan 1, 2025, 2:00:22 AMJan 1
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By the way…

One more interesting and quite unexpected relationship:

The sum of the first n integers CUBED is equal to the SQUARE of the sum of the first n integers!

In this case,




With best wishes, 
Steve 
_________________ 
Dr Stephen Arnold 
Educational Technology Consultant 
Compass Learning Technologies 
Web: http://compasstech.com.au 
_________________


On Wed, 1 Jan 2025 at 5:00 pm, 'Travis Bower' via tinspire <tins...@googlegroups.com> wrote:
fyi, typo page 1.3
Can you spot it?


Travis Bower, M.A.
Math Teacher
Dos Pueblos High School
tbower@sbunified.org
www.dphs.org
www.sbunified.org
805.968.2541 x4538

 


On Tue, Dec 31, 2024 at 3:15 PM John Hanna <johne...@gmail.com> wrote:

Found the attached problem via Google News today and had nothing better to do!

 

Happy New Year!

Regards,

     John

 

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With best wishes,
Steve
_________________
Dr Stephen Arnold
Educational Technology Consultant
Compass Learning Technologies

T3 Fellow, Teachers Teaching with Technology Australia

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Sent from my iPad

Stephen Arnold

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Jan 1, 2025, 2:03:04 AMJan 1
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Sorry - pasting an image didn’t work.

Sum(x,x,1,9) = 45

(Sum(x,x,1,9) = 45)^2 = 2025

Sum(x^3,x,1,9) = 2025

———————————-

John Hanna

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Jan 1, 2025, 6:18:30 AMJan 1
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Travis,

I don’t see it…

 

 

Regards,

     John

 

From: 'Travis Bower' via tinspire <tins...@googlegroups.com>
Sent: Wednesday, January 1, 2025 1:00 AM
To: tins...@googlegroups.com
Subject: Re: [tinspire] Happy New Year, wherever you are!

 

fyi, typo page 1.3

Can you spot it?

 

Travis Bower, M.A.

Math Teacher
Dos Pueblos High School

image001.png

Karlheinz Haas

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Jan 1, 2025, 10:41:54 AMJan 1
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John,
I think Travis may have been referring to Sean's "2025.tns" file.

Karlheinz

Sean Bird

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Jan 1, 2025, 10:44:25 AMJan 1
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Thanks. Found it. I’ll correct it later today 

Brendan Kelly

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Jan 4, 2025, 10:17:15 AMJan 4
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Thank you Stephen. This is one of the most beautiful identities in number theory.

Happy New Year!
Brendan


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Karen Campe

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Jan 5, 2025, 7:38:18 PMJan 5
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Steve, is that true in general? Everyone is pointing out that it's true for this year, because the results are both 2025...
WOW!
Karen

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Peter Petto

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Jan 5, 2025, 7:52:18 PMJan 5
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Yes it’s true in general, the same way that the sum of the first n odd numbers is n^2. Here’s a nice visual proof that’s similar to the 2D proof the odd-sum/square equivalence:

   —Peter


===
Peter Petto
Bay Village, OH





John Hanna

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Jan 5, 2025, 8:12:23 PMJan 5
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That never occurred to me!

Regards,

     John

 

From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of Peter Petto
Sent: Sunday, January 5, 2025 7:52 PM
To: tins...@googlegroups.com
Subject: Re: [tinspire] Happy New Year, wherever you are!

 

Yes it’s true in general, the same way that the sum of the first n odd numbers is n^2. Here’s a nice visual proof that’s similar to the 2D proof the odd-sum/square equivalence:

 

   —Peter

 

 

===

Peter Petto

Bay Village, OH

 

 

 

 

On Sun, Jan 5, 2025 at 7:38 PM Karen Campe <karen...@gmail.com> wrote:

Steve, is that true in general? Everyone is pointing out that it's true for this year, because the results are both 2025...

WOW!

Karen

On Wednesday, January 1, 2025 at 2:00:22 AM UTC-5 Steve A wrote:

By the way…

 

One more interesting and quite unexpected relationship:

 

The sum of the first n integers CUBED is equal to the SQUARE of the sum of the first n integers!

 

In this case,

 

With best wishes, 

Steve 

_________________ 

Dr Stephen Arnold 

Educational Technology Consultant 

Compass Learning Technologies 

_________________

 

 

On Wed, 1 Jan 2025 at 5:00 pm, 'Travis Bower' via tinspire <tins...@googlegroups.com> wrote:

fyi, typo page 1.3

Can you spot it?

 

Travis Bower, M.A.

Math Teacher
Dos Pueblos High School

Bird, Mr.

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Jan 5, 2025, 8:29:47 PMJan 5
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Nice youtube link. The IG short version https://www.instagram.com/share/__Q8AGAdW of Nicomachus's theorem is what prompted me to make the TI-Nspire interactive file 2025.tns (attached again) and make my IG post https://www.instagram.com/share/reel/BAU4tWRdve

Thanks,
Sean Bird

On Sun, Jan 5, 2025 at 7:52 PM Peter Petto <peter...@gmail.com> wrote:
Yes it’s true in general, the same way that the sum of the first n odd numbers is n^2. Here’s a nice visual proof that’s similar to the 2D proof the odd-sum/square equivalence:

   —Peter


===
Peter Petto
Bay Village, OH





On Sun, Jan 5, 2025 at 7:38 PM Karen Campe <karen...@gmail.com> wrote:
Steve, is that true in general? Everyone is pointing out that it's true for this year, because the results are both 2025...
WOW!
Karen

On Wednesday, January 1, 2025 at 2:00:22 AM UTC-5 Steve A wrote:
By the way…

One more interesting and quite unexpected relationship:

The sum of the first n integers CUBED is equal to the SQUARE of the sum of the first n integers!

In this case,
--

Mr. Bird
Teacher - Mathematics & Physics;
Adviser - NHS, Rocket Team, VEX Robotics; Coach - Boys & Girls Tennis

2025.tns
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