Geometry: Maximum or Minimum Perimeter?

  • Thread starter Thread starter googoogaagaa
  • Start date Start date
  • Tags Tags
    Geometry
AI Thread Summary
In the discussion, it is established that for a triangle with two legs of length 2, the maximum perimeter is not definitively 8 but is instead 7.999... (repeating), which is mathematically equivalent to 8 as it represents the least upper bound. The maximum angle of a triangle cannot reach 180 degrees, reinforcing the idea that no maximum perimeter exists. Similarly, for a rectangle with two opposite sides of length 2, the minimum perimeter is not strictly 4 but approaches 4, indicating that there is no minimum perimeter. Both cases illustrate the concept of limits in geometry, emphasizing that while values can approach certain bounds, they do not necessarily attain them.
googoogaagaa
Messages
1
Reaction score
0
If a triangle has two legs with lengths of 2 each, is the maximum permiter of that triangle 8, or 7.999 (repeating)? In other words, is the maximum angle of a triangle 180 degrees, or 17.999 (repeating) degrees?

Also, if a rectangle has two opposite sides with lengths of 2, is the minimum permiter of that rectangle 4, or 4.000000...1 (approching 4)?

Thank you!
 
Mathematics news on Phys.org
Mathematically its not too hard to prove (using infinite an series) that 7.9999... (on indefinitely) is the same as 8. Similarly for 4.00000...
 
In the first case, there is no maximum perimeter; however, 8 is the least upper bound of the possible perimiters of the triangle.

The second case is similar: no minimum perimeter.
 

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Geometry problem of interest with a 3-4-5 triangle
2
Replies
59
Views
2K
I Chiral symmetries in E[SUP]^n[/SUP]
Replies
1
Views
2K
MHB Is there a formula for finding the perimeter of a triangle with known vertices?
Replies
3
Views
2K
MHB Find the height and base of a trapezium
Replies
1
Views
2K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
Replies
2
Views
1K
B What is the name of this triangular geometric shape?
Replies
2
Views
2K
MHB Determine the ratio of the base to the perimeter.
Replies
2
Views
4K
MHB Find the areas of segment in circle
Replies
1
Views
2K
Perimeter relationships -- Dividing a rectangle into 4 triangles
Replies
2
Views
2K
MHB Maximum area of triangle and quadrilateral - given perimeter
Replies
6
Views
7K

Hot Threads

Recent Insights

Back
Top