Solving Semi-circle Inside Triangle Geometry Problem

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Discussion Overview

The discussion revolves around a geometry problem involving a semi-circle inscribed within a triangle, where the triangle has known side lengths and the goal is to determine the radius of the semi-circle and its position along the base of the triangle. The problem is framed in the context of evaluating the capabilities of AI tools like ChatGPT and Bing Chat in solving geometric problems.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a geometry problem involving a semi-circle inside a triangle, seeking equations for the radius and position of the semi-circle based on the triangle's dimensions.
  • Another participant suggests that the current AI tools may not provide reliable mathematical results, particularly in geometry.
  • Several participants express skepticism about the reliability of AI in solving geometry problems, citing past experiences where AI provided incorrect answers.
  • There are comments about the hype surrounding AI capabilities, with some comparing it to the sales tactics of used car salesmen.
  • One participant mentions that the problem requires analytic geometry, implying that AI may lack the necessary depth in this area.
  • Another suggests a systematic approach to testing AI capabilities by starting with simpler questions before progressing to more complex ones.
  • Some participants note that while AI can struggle with geometry, it may perform adequately with simpler arithmetic tasks.
  • A participant reflects on the nature of AI responses, indicating that AI can only echo existing proofs or knowledge available online.

Areas of Agreement / Disagreement

Participants generally express skepticism about the ability of AI to solve the geometry problem effectively, with multiple competing views on the reliability of AI tools in mathematical contexts. The discussion remains unresolved regarding the specific capabilities of AI in this area.

Contextual Notes

Participants highlight limitations in AI's ability to handle complex geometric problems and suggest that the effectiveness of AI may depend on the nature of the questions posed.

mathman
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TL;DR
AI cannot do geometry!
Gave following to bing chat and chatgpt, Both gave wrong answers. Any thoughts?
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Geometry problem: Semi-circle inside triangle: Triangle with known length sides a, b, c where a is the longest. Place inside the triangle a semi-circle with entire diameter resting on side a, which is horizontal. The arc of the semicircle is maximum possible inside the triangle.
Known - triangle dimensions. Unknown r (semi-circle arc radius) and x (distance along a from left end of a to center of diameter). Find equations for r and x In terms of all possible triangles.
 
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You'll likely need to wait for the Wolfram Alpha plugin to get out of early access for more confident math results.
 
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mathman said:
TL;DR Summary: AI cannot do geometry!

Any thoughts?
Certainly, despite the "AI" claim, ChatGPT doesn't have any.
 
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There are over a dozen threads here of the form "ChatGPT gets this wrong!" "And this!" "And this too!". To me the surprise isn't that it gets things wrong; it's that it sometimes gets them right.

Maybe it would be best to consolidate all these threads.
 
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Vanadium 50 said:
There are over a dozen threads here of the form "ChatGPT gets this wrong!" "And this!" "And this too!". To me the surprise isn't that it gets things wrong; it's that it sometimes gets them right.
I'd like to say I was surprised by the surprise, but it's easy to get swept up in the hype. After learning the basics of how it works though, I share your take. Maybe when linked to real knowledge sources/tools (like Wolfram Alpha) it will have some reliability.
 
I detect a similarity between ChatGPT hype and the words emitted by a used car salesman. :eek:
 
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Except that used car salesmen occasionally have actual cars.
 
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My question requires analytic geometry. AI (chatgpt or Bingchat) don;t have it.
 
I asked the AI to give my life purpose, and it didn't know how. I was so disappointed. :rolleyes:
 
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  • #10
mathman said:
My question requires analytic geometry. AI (chatgpt or Bingchat) don;t have it.
If you want to be more systematic in testing their capabilities, you should try first asking them elementary questions about the constructions in your problem, and then gradually make the task more difficult.
 
  • #11
Greg Bernhardt said:
You'll likely need to wait for the Wolfram Alpha plugin to get out of early access for more confident math results.
why wait https://www.wolframalpha.com/downloads.

ChatGPT is easily confused with operators in math as a large language model.
 
  • #12
I don't think ChatGPT can do geometry, although it can do very simple arithmetics.
 
  • #13
If enough people put a proof on the web, ChatGPT can echo it back.

In the words of John Entwistle:

Everything I do has been done before
Every sentence in my head,
Someone else has said.
 

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