Check Out This Incredible Math Trick

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Discussion Overview

The discussion revolves around a mathematical trick involving shapes and areas, specifically focusing on the conditions under which certain shapes can be classified as rectangles. Participants explore the implications of slopes in relation to the geometry presented in a linked video.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant shares a link to a math trick, expressing enthusiasm about its content.
  • Another participant critiques the trick, stating that for the shape to be a rectangle, the slopes of the triangles must be equal, which they calculate as 3/8 and 2/5, respectively.
  • This participant concludes that since the slopes do not match, the shape cannot be a rectangle, and thus the area cannot be determined by multiplying the sides.
  • A later reply acknowledges the amusement of the trick but does not address the mathematical critique.
  • One participant reiterates the earlier critique, questioning the area of a triangle within the supposed rectangle and attempts to identify its vertices, but ultimately expresses uncertainty about the correctness of their assessment due to the changing slope.

Areas of Agreement / Disagreement

Participants express disagreement regarding the classification of the shape as a rectangle and the validity of the area calculation. Multiple competing views remain, particularly concerning the implications of the slopes and the geometry involved.

Contextual Notes

The discussion includes assumptions about the properties of shapes and slopes, and the validity of the area calculations is unresolved. The participants' interpretations of the geometry may depend on specific definitions and visual representations not fully detailed in the posts.

Econometricia
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Sorry if this has been posted. Thought it was cool!
http://www.wimp.com/crazymath/
 
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Bit different version of a old rube.

For the created shape to be a rectangle you need to have the slopes of the red and green triangles (3/8) be equal to the slope of the angle of the other 2 shapes (2/5).

Since .4 <> .375 that is not a rectangle and you cannot get the area by multiplying sides.
 


But still amusing!
 


Integral said:
Bit different version of a old rube.

For the created shape to be a rectangle you need to have the slopes of the red and green triangles (3/8) be equal to the slope of the angle of the other 2 shapes (2/5).

Since .4 <> .375 that is not a rectangle and you cannot get the area by multiplying sides.

So is it safe to say that in the 5x13 "rectangle", there is a triangle of area ONE unit with a vertex in the top right corner and two vertices near the bottom left corner?

edit...
No, that can't be right, since the slope changes from 3/8 to 2/5...
So vertices:
1) top right corner (13, 5)
2) at "point" (5,2)
3) bottom left corner (0,0)
 

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