No doubt as some people have already seen, today morning wolfram posted the best valentine ever. The graph depicting cupid with its arrow and floating hearts around it involves something like 6 pages of parametric equations. My question to this community is, does any one have any idea how these equations were discovered? Is there a methodology here when people post equations with graphs looking like bunnies or hearts or is it just playing around with trigonometric functions with a little bit of intelligent guessing until something interesting pops out? Are there an papers/books/references on these type of derivations? No doubt these have been done for a while. I hope somebody at wolfram will publish something soon.
2026-04-06 20:43:35.1775508215
How are the parametric equations describing the cupid curve derived?
785 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in TRIGONOMETRY
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- Finding the value of cot 142.5°
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$
- Sine of the sum of two solutions of $a\cos\theta + b \sin\theta = c$
- Tan of difference of two angles given as sum of sines and cosines
- Limit of $\sqrt x \sin(1/x)$ where $x$ approaches positive infinity
- $\int \ x\sqrt{1-x^2}\,dx$, by the substitution $x= \cos t$
- Why are extraneous solutions created here?
- I cannot solve this simple looking trigonometric question
Related Questions in PARAMETRIC
- Suggest parametric equations for a given curve
- Parametric Circle equations and intersections
- Is it possible to construct the equation of a surface from its line element?
- Finding the equation of aline in implicit form
- Finding whether a parametric curve has a well defined tangent at the origin
- Parametric representation of a cylinder generated by a straight line
- Converting circle parametric equation
- Finding the major and minor axes lengths of an ellipse given parametric equations
- Draw (2, 3) torus knot on the unwrapped torus surface
- Question about parametric, implicit equation and vector equation
Related Questions in GRAPHING-FUNCTIONS
- Lower bound of bounded functions.
- Do Irrational Conjugates always come in pairs?
- Graph rotation: explanation of equation
- Plot function y = tan(yx)
- Sketching a lemniscate curve with a max function?
- 3 points on a graph
- show $f(x)=f^{-1}(x)=x-\ln(e^x-1)$
- What is this method of sketching a third degree curve?
- Getting a sense of $f(x) = x (\log x)^6$
- Can I describe an arbitrary graph?
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?
http://en.wikipedia.org/wiki/Spline_%28mathematics%29 and http://en.wikipedia.org/wiki/Vector_graphics
Wolfram's Cupidon was made by trigonometrical "parts". Anyway, the basic idea is the same as with polynomial splines. Take any advanced vector graphics editor (or modify or make such) - and you will get automatic derivation of such equations.
And heavy use of Heaviside Step Function in it (http://mathworld.wolfram.com/HeavisideStepFunction.html), if I'm correct, is only for masking/merging such fragmentation.