Geometry, an age-old branch of mathematics, concerns itself with questions of size, shape, relative positions of figures, and properties of space.

While it’s a vast topic with myriad terms, today, we’ll journey through the niche of those that begin with the letter ‘O’.

Here we go:

## Geometry Words Starting In O

1. Obtuse angle – An angle greater than 90° but less than 180°.
2. Origin – A fixed reference point from which distances or angles are measured.
3. Oval – A shape resembling an egg or an ellipse.
4. Octagon – A polygon with eight sides and eight angles.
5. Octahedron – A polyhedron with eight faces.
6. Orthogonal – Being perpendicular or relating to right angles.
7. Orthocenter – The point where the altitudes of a triangle intersect.
8. Orbit – In geometry, it is the path a point takes around another fixed point.
9. Ordinate – The vertical coordinate of a point, especially in a two-dimensional Cartesian system.
10. Oblique – Neither perpendicular nor parallel; slanting.
11. Obliquity – The angle between the plane of an orbit and a reference plane.
12. Opposite sides – Sides that are directly across from each other in a polygon.
13. Octant – One of eight sectors created when three mutually perpendicular planes intersect.
14. Opposite angles – Angles opposite each other when two lines intersect.
15. Orthogonal projection – A projection of a figure onto a plane by drawing perpendiculars from the points of the figure to the plane.
16. Offset – A short distance measured perpendicular to the main direction.
17. Orientable – A surface that possesses a consistent ‘up’ and ‘down’.
18. Octahedral angle – The angle between any two edges of an octahedron, about 109.47°.
20. Octagonal prism – A prism with octagonal bases.
21. Ogee curve – An S-shaped curve.
22. Obelisk – A tall, four-sided pillar that tapers upwards and ends in a pyramid.
23. Obtuse triangle – A triangle with one obtuse angle.
24. Outer circle – The circumscribed circle that touches all vertices of a polygon.
25. Octal system – A base-8 number system, not strictly geometrical but used in certain geometrical computations.
26. Octagonal pyramid – A pyramid with an octagonal base.
27. Order – In geometry, it often refers to the number of times a geometric object intersects another.
28. Orientation – The arrangement or alignment of a shape in relation to its surroundings or another shape.
29. Outlier – A point or value that differs substantially from others in a data set.
30. Orthonormal – Describes a set of vectors that are both orthogonal and normalized.
31. Osculating circle – A circle that touches a curve at a point and has the same curvature as the curve at that point.
32. Octadic – Pertaining to the number eight, as in an octadic angle division.
33. Orthodiagonal – Pertaining to a quadrilateral where the diagonals are perpendicular.
34. Osculation – The act of fitting a curve to another curve or surface.
35. Octahedral symmetry – The symmetry operations that preserve an octahedron.
36. Overshoot – The amount a curve or surface extends beyond its expected end or limit.
37. Orbifold – A generalization of manifolds allowing for certain singularities.
38. Orthogonal transformation – A linear transformation that preserves lengths.
39. Optical geometry – A system that describes how light rays propagate in a linear fashion.
40. Obtuse hyperbola – A hyperbola where the angle between the asymptotes is obtuse.
41. Obtuse parabola – A term occasionally used to describe certain configurations in parabolic geometry.
42. Octadecagon – An 18-sided polygon.
43. Octonion – A kind of non-associative algebra over the real numbers.
44. Optimal design – The study of designing experiments.
45. Orthogonal matrix – A square matrix whose rows and columns are orthogonal vectors.
46. Orthonormal basis – A set of vectors which are mutually orthogonal and each of unit length.
47. Outscribed – Enclosing or encircling a shape, often referring to circles around polygons.
48. Oriented angle – An angle that determines the rotation direction (clockwise or counterclockwise).
49. Octagon tessellation – A tiling of the plane using octagons.
50. Octahedron tessellation – A 3D tiling using octahedra.

While geometry might seem abstract and challenging, the beauty lies in how these concepts shape our world, both natural and constructed.

Understanding these ‘O’ terms offers a fascinating window into the complexity and artistry of this mathematical discipline. Whether you’re a seasoned geometer or a casual enthusiast, may this list serve as a bridge to deeper exploration.

1. Oblique cone – A cone that is not a right cone, meaning its apex is not aligned directly above the center of its base.
2. Oblate – Flattened at the poles; usually referring to spheroids.
3. Octic – Referring to the eighth degree, especially a polynomial.
4. Off-center – Not positioned in the middle or not aligned.
5. Overlapping – Geometric figures covering some of the same space.
7. Obtuse sector – The portion of a circle bounded by an obtuse angle and its associated arc.
8. Orthogonal complement – A subspace where every element is orthogonal to a given subspace.
9. Octacontagon – A polygon with 80 sides.
10. Octilinear – Pertaining to paths or figures defined by straight lines and octagonal symmetries.
11. Outlying – Positioned at a greater distance from the center.
12. Octadic division – Splitting a shape or figure into eight equal parts.
13. Outcurve – A curve that bends outward from a central point or line.
14. Oversketch – A rough drawing over an existing geometric figure to study alterations.
15. Octahedral angle – The angle made between any two adjacent edges of an octahedron.
16. Orthocyclic – Circles that intersect at a single, shared point.
17. Orthonormal transform – A transformation that maintains orthonormality.
18. Oblique prism – A prism with bases that are not aligned directly above each other.
19. Octagram – An eight-pointed star figure.
20. Outpolygon – A polygon that encloses one or more other polygons.
21. Outangle – An angle formed by rays extending outward from a figure or shape.
22. Octaplane – A plane divided into eight regions or sectors.
23. Octaspace – An eight-dimensional geometric space.
24. Omnioriented – Oriented in all possible directions.
25. Orthogonally adjacent – Neighboring in a manner that is aligned with the primary axes.
26. Oversized angle – An angle larger than what’s typical or standard in a given context.
27. Oblate ellipsoid – An ellipsoid flattened along its major axis.
28. Octadecahedron – A solid figure with 18 faces.
29. Octant sector – One-eighth of a circular region.
30. Orthogonalize – To make vectors or functions orthogonal to each other.
31. Osculating plane – The plane that touches a curve or surface at a point.
32. Octocycle – A closed figure with eight straight or curved segments.
33. Octaedral network – A network of lines and intersections that form octahedral patterns.
34. Outrigon – An external triangle connected to another geometric shape.
35. Outpoint – A point located outside a specific geometric figure.
36. Octagonal frustum – The portion of an octagonal pyramid or cone between two parallel planes cutting it.
37. Outradius sector – A sector formed by extending the outradius of a polygon.
38. Oblate cylinder – A cylinder that’s shortened or compressed along its height.
39. Overslope – A slope or incline that exceeds a specified amount.
40. Orthotope – A generalization of a rectangle to higher dimensions.
41. Open curve – A curve that does not return to its starting point.
42. Orbit curve – The trajectory of a point under a series of geometric transformations.
43. Outvertex – A vertex positioned on the exterior of a geometric shape.
44. Orbital ellipse – An elliptical trajectory, particularly relevant in celestial mechanics.
45. Outcuboid – An external rectangular prism associated with another 3D figure.
46. Orthohedron – A 3D shape whose faces are all orthogonal to one another.
47. Octal segment – One of eight parts of a divided geometric figure.
48. Octagonal spire – A pinnacle or tower with eight sides, commonly seen in architecture.
49. Overarc – A part of a curve that extends beyond a specified or intended endpoint.
50. Orthogonal hyperbola – A hyperbola resulting from an intersection of a double cone with a plane perpendicular to its axis.

## Conclusion

Navigating the landscape of geometric terms is like exploring a labyrinth filled with patterns, symmetry, and unique structures. From the simplicity of the oval to the complexity of the octahedron, the vast world of ‘O’ terms in geometry is a testament to how intricate and profound this field of study can be.