What is the largest possible number of acute angles

  • Thread starter Thread starter 22-16
  • Start date Start date
  • Tags Tags
    Angles
Click For Summary
SUMMARY

The largest possible number of acute angles in a 2001-gon can reach up to 1334 internal acute angles, as established by the user Hurkyl. Additionally, if external angles at concave vertices are considered, the number of acute angles can increase to 2000, with the potential for a 2001st acute angle. This discussion clarifies the distinction between internal and external angle measurements in polygon geometry.

PREREQUISITES
  • Understanding of polygon geometry
  • Knowledge of acute angles and their properties
  • Familiarity with concave and convex vertices
  • Basic principles of angle measurement
NEXT STEPS
  • Research the properties of concave polygons
  • Explore the concept of internal vs. external angles in polygons
  • Study the implications of angle measurement on polygon classification
  • Investigate the maximum angle configurations in higher-gon shapes
USEFUL FOR

Mathematicians, geometry enthusiasts, and educators looking to deepen their understanding of polygon properties and angle classifications.

22-16
What is the largest possible number of acute angles that a 2001-gon (shape with 2001 sides) can have if no two sides cross each other [?]
 
Last edited by a moderator:
Mathematics news on Phys.org
Depends on how you measure the angles.

If the angle at a concave vertex is measured externally to the polygon, then I can give you 2000 acute angles, and can probably give you the 2001-st as well.

Hurkyl
 
It is possible to make a 2001-gon with 1334 acute internal angles.
 

Similar threads

MHB Proving Equality of Angles in an Acute Triangle
  • · Replies 4 ·
Replies
4
Views
1K
MHB Acute angle of right triangles
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
  • · Replies 2 ·
Replies
2
Views
1K
MHB Forces of 8N: Find Angle & Mass of Particle
  • · Replies 4 ·
Replies
4
Views
2K
MHB Why is Angle C Assumed to be Acute and What is the Value of Sin C in ∆ABC?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Solving Acute Triangle Angles Given $A,B,C$ & Equations
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Criticism of the doctrine of infinity
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Cross product or vector product.
  • · Replies 5 ·
Replies
5
Views
2K
MHB Dimension of the cut-out squares that result in largest possible side area
  • · Replies 3 ·
Replies
3
Views
3K
MHB What is the relationship between secant and cosecant in terms of acute angles?
  • · Replies 2 ·
Replies
2
Views
2K