Solve Prof. John Mentriffe's Triangle Puzzle

  • Context: Undergrad 
  • Thread starter Thread starter anvesh111
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Discussion Overview

The discussion revolves around a puzzle presented by Prof. John Mentriffe regarding right-angled triangles and their area, which challenges established geometric norms. Participants explore the implications of this theory and its potential impact on the understanding of area in mathematics, particularly in relation to motion and the design of the Universe.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant notes that the puzzle challenges the accepted notion that the area of a shape remains constant regardless of how its parts are arranged.
  • Another participant references an optical illusion related to triangles, suggesting that careful observation reveals discrepancies in the hypotenuses of the shapes presented.
  • A different participant identifies that the triangles in question have different slopes and side ratios, indicating that they are not congruent triangles.
  • Some participants discuss the nature of optical illusions and how perception can be misleading, particularly regarding straight lines and angles.
  • There is a repeated reference to the same optical illusion link, emphasizing the need for close examination of the shapes involved.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the triangles and the implications of the optical illusion, indicating that there is no consensus on the interpretation of the puzzle or its theoretical implications.

Contextual Notes

The discussion includes assumptions about visual perception and geometric properties that are not fully explored or resolved, particularly regarding the implications of the optical illusion on the understanding of area.

anvesh111
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INTERESTING PUZZLE ANY ANSWER?
Please find solution.

We have learned from our childhood that area of an entire body (triangle, circle, rectangle etc) is equal to the sum of area of the parts it contains... and even if these parts are arranged differently, the area remains unchanged... but this mail challenges this fact... Do let me know if you get an answer for this one...

Here's a puzzling new discovery:
Recently a professor in MIT has put a new theory on right-angled triangles that has challenged some accepted norms in Geometry. This theory, Prof. John Mentriffe says, will revolutionize area in mathematics that deals with calculation of motion objects in space and design of the Universe.
 

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Mathematics news on Phys.org
oh i see it, they are not triangles. both the small triangles have different slopes. one triangle has a side ratio of 2:3 and another 8:3
 
It's an optical illusion, our eyes like to see straight lines, and we usually don't notice that they bulge or tuck unless we are told to...
 

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