In NJ Wildeberger's book (which I don't see much use in citing, since its an offline material, so instead I will provide a link to his key points further down) he argues that "Quadrance" can be just as useful as "Distance". He defines Quadrance as: "A squared plus B squared" & "(((C - A)^2)+((B - D)^2)) given lines 'AB' and 'CD'. More info here: " https://www.quora.com/Is-N-J-Wildberger-a-joke-or-a-genius-when-he-claims-that-mathematics-in-its-current-form-is-a-hoax " & here: " https://en.m.wikipedia.org/wiki/Rational_trigonometry " . Now knowing quadrance fills the shoes of distance; what fills the shoes of area? And how can it be converted back into its 'non-rational' equivalent?
2026-04-08 00:50:47.1775609447
How does quadrea relate to area?
269 Views Asked by user21982 https://math.techqa.club/user/user21982/detail At
1
There are 1 best solutions below
Related Questions in GEOMETRY
- Point in, on or out of a circle
- Find all the triangles $ABC$ for which the perpendicular line to AB halves a line segment
- How to see line bundle on $\mathbb P^1$ intuitively?
- An underdetermined system derived for rotated coordinate system
- Asymptotes of hyperbola
- Finding the range of product of two distances.
- Constrain coordinates of a point into a circle
- Position of point with respect to hyperbola
- Length of Shadow from a lamp?
- Show that the asymptotes of an hyperbola are its tangents at infinity points
Related Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related Questions in QUADRATICS
- Do you have to complete the square before using the quadratic formula?
- Roots of the quadratic eqn
- Questions on positivity of quadratic form with orthogonal constraints
- Conjugate quadratic equations
- Do Irrational Conjugates always come in pairs?
- Quadratic Equations and their roots.
- Solving a quadratic equation with square root constants.
- What would the roots be for this quadratic equation $f(x)=2x^2-6x-8$?
- Polynomial Equation Problem with Complex Roots
- Solve $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ and avoid extra solutions while squaring
Related Questions in RATIONAL-NUMBERS
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- I don't understand why my college algebra book is picking when to multiply factors
- Non-galois real extensions of $\mathbb Q$
- A variation of the argument to prove that $\{m/n:n \text{ is odd },n,m \in \mathbb{Z}\}$ is a PID
- Almost have a group law: $(x,y)*(a,b) = (xa + yb, xb + ya)$ with rational components.
- When are $\alpha$ and $\cos\alpha$ both rational?
- What is the decimal form of 1/299,792,458
- Proving that the sequence $\{\frac{3n+5}{2n+6}\}$ is Cauchy.
- Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.
- What is the identity element for the subgroup $H=\{a+b\sqrt{2}:a,b\in\mathbb{Q},\text{$a$ and $b$ are not both zero}\}$ of the group $\mathbb{R}^*$?
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?
The definition of quadrea is $ (Q_1+Q_2+Q_3)^2-2(Q_1^2+Q_2^2+Q_3^2).\;$ If $\;d_21^2=Q_1,\;$ $d_2^2=Q_2,$ $d_3^2=Q_3$, then it is $(d_1+d_2+d_3)(-d_1+d_2+d_3)(d_1-d_2+d_3)(d_1+d_2-d_3)$ and by Heron's formula this is $16$ times the square of the area of the triangle.
This can be checked by looking at an equilateral triangle side $d$ whose area squared is $\frac3{16}d^4.$