I Math Myth: The sum of all angles in a triangle is 180°

Greg Bernhardt
Admin
Insights Author
Messages
19,773
Reaction score
10,726
From @fresh_42's Insight
https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/

Please discuss!

We all live on a globe, a giant ball. The angles of a triangle on this ball add up to a number greater than ##180°##.

Kugeldreieck.png


And the amount by which the sum extends ##180°## isn't even constant. It depends on the size of the triangle. The flat triangle with angle-sum ##180°## is the exception, not the norm. The real world is crooked.
 
Last edited by a moderator:
Mathematics news on Phys.org
This is something I never knew in school! Has anyone else heard of this before?
 

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 '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 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

B A Question Relating Sum of Angles and Breaking of the Parallel Postulate
Replies
6
Views
1K
I Math Myth: Parallels do not intersect
Replies
3
Views
2K
I Is 360° Really the Correct Measurement for a Full Angle?
Replies
2
Views
1K
MHB Internal angle sum of triangle
Replies
1
Views
2K
I Math Myth: Reducing an equation
Replies
4
Views
1K
I Math Myth: The rationals are numbers
3
Replies
142
Views
9K
I Math Myth: A prime is only divisible by 1 and itself
Replies
4
Views
2K
Geometry (Proof right triangle angle sum is 180)
Replies
4
Views
9K
I Math Myth: You cannot divide by 0
Replies
5
Views
2K
I Math Myth: ##0.999999999.... =0.\bar{9}= 1##
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top