2.1.1 Variation on Johnson Jackson Pythagorean Theorem 1
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- เผยแพร่เมื่อ 7 มิ.ย. 2024
- Variation on Johnson Jackson Pythagorean Theorem 1.
The inspiration for this video is given to Calcea Johnson and Ne’Kiya Jackson at the link:
rajivsethi.substack.com/p/the...
At the time of making this video, I did not have access to the the original work of these authors, but I have seen many related videos, posted below.
Related TH-cam videos:
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60 Minutes Documentary, posted circa May 6, 2024:
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Desmos:
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The thumbnail is a screenshot from polymathematic's Desmos diagram.
MathyJaphy has a nice proof of the Geometric Series.
LindaGreen has a nice proof of the sum angles formulae.
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
My understanding is that Johnson and Jackson developed two separate methods; Jackson, I think, did hers using a circle, Johnson did the infinite right triangle waffle cone.
I just watched the 60 Minutes video featuring Calcea Johnson and Ne’Kiya Jackson. Thank you.
There's an Johnson theorem and there's a Jackson theorem. This is only one of them. I'd appreciate it if you did a video on the other one.
God willing, I shall make another video, based on Ne’Kiya Jackson's circle proof. Thank you for watching my video. Lately, the number of views of my video has increased. I wonder if the 60 Minutes documentary has something to do with it.
@@theoremus Jackson's proof is almost exactly the same as proof 60 at cut-the-knot.
Beautiful, great !
They have since found 2 more answers. Using the circle they possibly have found 5 more.
I'm new to this channel! Love your content! Im just an engineer learning advanced math... thank you!
@xaviergonzalez5828 Salvete! I am also learning math (Algebraic Calculus) and Latin language. I would like to teach my math in Latin. Do you think that more people would watch my channel if I taught in Latin?
@@theoremus of course!
Nice job dad! 👍
Thanks!
Cheers Marian, the mic helps a lot with the audio!
Thanks, my next investment is to obtain a software graphics tool to do my math presentations. In math videos, you do not need a camera, just a mic and drawing tool is needed.
Very nice. Very quadrature-y!
Rob, it is good to hear from you again. Have you watched my videos on quadrature, using polynumbers? I am considering to create a short course on quadrature. It would be better organized and faster pace than my existing playlist. I value your input.
@@theoremusHi! I made a long-ish reply, but it looks like TH-cam may have blocked it or put it in your 'spam' comments or something, however that works. Maybe you'll need to manually unblock it? Maybe check inside your channel account.
Rob, perhaps the comment was too long. I have an email address listed at orcid.org/0000-0003-4551-7516
You can contact me via email. If you are working on something exciting, then publish it on your TH-cam channel.
haha a new way for me to proof the classic pythagoreann theorem yeay ! XD
There is more.
@@theoremus a lot... more ;-; way over 370 ;-;; sir imaginee an asmr video going through all those proovings! :D
@@theoremus Sorry, but I see I a flaw in this waffle cone ''triangle''. The extendeed series never end, therefore, the extended lines never physically intersect. Also, why is the waffle shaped cone extended to the right? If you created another triangle by placing a cone right beneath the original triangle the results would be different. Also, this juggling of triangles inside of triangles is done rather by algebra and not trigonometry until you hit the Pythagorean theorem by kaleidoscopic effect.
Sorry, but I see I a flaw in this waffle cone ''triangle''. The extendeed series never end, therefore, the extended lines never physically intersect. Also, why is the waffle shaped cone extended to the right? If you created another triangle by placing a cone right beneath the original triangle the results would be different. Also, this juggling of triangles inside of triangles is done rather by algebra and not trigonometry until you hit the Pythagorean theorem by kaleidoscopic effect.
Calcea Johnson & Ne’Kiya Jackson..
I have posted a credit to the both authors in my video description. I have also put a link to a 60 Minutes video. Thank you for watching my video. May I ask what drew you to my video? Lately the number of views on my video has increased much.
😂haven't looked at the video? Really? Wow!😂, shameful!
I have seen other peoples videos, but I have not seen any video from Johnson and Jackson. Can you post a link to their video, please?
I’d think their videos wouldn’t be hard to find. 60 Minutes did a story with both girls who explained their individual approach.
th-cam.com/video/VHeWndnHuQs/w-d-xo.htmlsi=h8gf_lU-aSlbOXCd
Thank you. I have just watched the 60 Minutes video. I think that I can figure out Ne’Kiya Jackson's circle based proof. I look forward to making another video, based on the circle proof.
You seem to be lampooning their method yet they did what you and many have failed for 2500 years. Give those two black girls some credit because if they had shot someone, everyone would know their faces. You have just made a mess of one of the girl's methods and there is no variation at all. In fact, that is just one method because another one uses circles.
Please allow me to respond:
"You seem to be lampooning their method" - I am not lampooning their method, nor did I intend for it to “seem” that way. This is a great accomplishment on the part of Johnson and Jackson! I love math and their proof caught my eye, I have enjoyed studying it and was excited to share a variation of it. I do math videos for fun and I try to incorporate an element of humor into my math. You can observe this in my other videos.
"Give those two black girls some credit" - I have given Calcea Johnson and Ne’Kiya Jackson credit in the description, also during the video at 0:32, 2:26, and 9:24 and following. They have done great work! Please watch my video and see the links in the description.
"You have just made a mess of one of the girl's methods" - I am a software engineer; in software engineering, we employ code reviews. In mathematics, similar processes occur. Any critiques are not meant to be taken personally.
"there is no variation at all" - I’d respectfully disagree with you here, there are many variations out there based on one waffle cone setup. Some use area, trig and calculus. Others use just trig and calculus. Some use linear algebra (Meisters formula). Some use the Law of Sines. Some use Sum and Difference Angle formulas. I have included the links to some other related videos in the description that show different variations. What Calcea Johnson and Ne’Kiya Jackson have done is the creation of an entire class of Pythagorean Theorem proofs, not just one proof.
In conclusion, I congratulate Calcea Johnson and Ne’Kiya Jackson for their accomplishment! Good job!
Technically, it's not a pure trig proof so they actually failed too.
Such claims of it being pure trigonometric is subjective depending on how strict or loose you want to be with the definition of "Trigonometry." If you take a very strict definition of trigonometry then it's not a pure trigonometric solution like they are claiming. If you take a looser interpretation then many other proofs could equally be called "trigonometric."
Also, Jason Zimba's proof is not the only proof out there that only uses only trigonometry.
For the record, all they did is take a KNOWN geometric series and add a triangle on top. Their solution is more the result of luck and it's really only superficially trigonometric because the little trig that is in the proof isn't even needed. Neither is the triangle they added to the top for that matter.
@@theoremus "Of course, you lampooned it. First, you began your video with the entire triangle already drawn out while covering your so-called alternative proof, without mentioning exactly how they thought through the idea. Their proof is a trigonometric proof of the Pythagorean Theorem, which is significant because, for over 2,500 years, it was believed that a pure trigonometric proof of the theorem was impossible. But why was this the case?
The belief stemmed from the understanding that any trigonometric proof of the Pythagorean Theorem would inevitably rely on the Pythagorean identities, specifically
sin^2(𝑥)+cos^2(𝑥)=1. This identity itself is derived from the Pythagorean Theorem, leading to a circular argument if used in a proof purported to be independent of the theorem.
However, these students managed to derive a trigonometric statement of the form 2𝑎𝑏/sin(2𝑎)=𝑐^2 , which ultimately fits with 𝑎^2+𝑏^2=𝑐^2. Their approach bypassed the traditional reliance on Pythagorean identities, offering a novel angle to the proof. Dismissing their proof without properly presenting and analyzing their methodology is lampooning their significant academic achievement and the potential it holds for mathematical discourse. Either you didn't understand it, or you were lampooning it
You have not given them any credit! You admitted at 3:12 that you have not seen their work and are basing your video on what others have done. Why not review their work directly before proposing a so-called variation of their proof considering that no one has ever done this in 2500 apart from Jonas Zimba? By not doing so, you are misrepresenting their ideas and contributions. It is only fair and academically honest to engage with their original work to understand their thought process fully and to give them the recognition they deserve for their innovative approach.
You have just made a mess of the equation, and your so-called variation is essentially a copy of what the girls did. If you are indeed confident that your variation is unique and not derived from their method, I challenge you to submit it for peer review. Only through rigorous academic scrutiny can the originality and validity of your work be established.
As things stand, your approach reeks of intellectual dishonesty. By presenting a variation without properly acknowledging its resemblance to the original proof, you are undermining your own credibility and that of your work and unfairly overshadowing the students' innovative contribution. I urge you to either take down this video or revise it to accurately reflect the original authors' contributions and provide a clear distinction if your method is genuinely different