I'm looking for a reference on the theory of straightedge and compass constructions in three dimensions akin to Euclid's Elements in two dimensions. More specifically, I mean a theory of geometric constructions where one is allowed lines between any two points, planes through any three non-colinear points, and spheres with a given center and radius. My preliminary Google searches aren't giving anything but surely this has been studied.
2026-03-27 07:48:08.1774597688
Straightedge and compass theory in three dimensions
460 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in GEOMETRIC-CONSTRUCTION
- Construction of a graph from cycle $C_6$ and $C_7$ with specific properties (of specific eccentricities)
- Sequence of folds for finding intersection of two circles, given centers/radii
- Construct a triangle given a height, his base and the opposite angle
- Given the angles and diagonals of a quadrilateral, construct the quadrilateral using only a straightedge, a pencil, and a compass
- Proof of construction of inscribed regular hexagon
- Geometrically construct sides on cube
- When are we supposed to use 'constructions' in mathematical geometery proofs?
- Ruler and compass construction field extension
- What is this "easy application of the Pythagorean theorem"?
- Make a 60° angle on line $l$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
I think the first chapters of Elementary Geometry by John Roe could be useful. According to the Preface the first and the third chapter use a "classical approach, starting from fundamental properties of parallelism, measurement, and so on", whereas the rest of the book uses the "algebraic approach", i.e. analytic geometry. At the end there is also a list of references.