#quadratic — Public Fediverse posts

Quadratic memory reductions for Zero-knowledge Proofs

https://github.com/logannye/space-efficient-zero-knowledge-proofs

#HackerNews #Quadratic #Memory #Reductions #Zero-Knowledge #Proofs #Cryptography #Blockchain #Research

Quadratic memory reductions for Zero-knowledge Proofs

https://github.com/logannye/space-efficient-zero-knowledge-proofs

#HackerNews #Quadratic #Memory #Reductions #Zero-Knowledge #Proofs #Cryptography #Blockchain #Research

@jwildeboer All the "we promise not to be evil" megacorps made an instant about face when they realized they needed to build a nuclear reactor to power their "AI Datacenter". It's pretty juicy.

The problem is, they are assuming that the current technology scales, which is rather obviously a little bit dumb. Your brain needs about 30 watts, not a 30 MW Datacenter

Transformers are O(n^2). The solution is *never* going to be "just make n bigger".
By the time your datacenter is half built, some 24 year old will figure out an architecture that blows Transformers out of the water

#quadratic #transformer #brains

Why weren't you taught the cubic formula?
https://www.youtube.com/watch?v=N-KXStupwsc
#Mathologer #BurkardPolster @Mathologer
#NumberTheory #algebra #geometry
#quadratic #cubic #polynomial
#maths #mathematics #education
#math

One day, one decomposition
A198773: Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A198773.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A198773.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #representations #quadratic #form #graph #threejs #webGL

One day, one decomposition
A198773: Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A198773.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A198773.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #representations #quadratic #form #graph #threejs #webGL

One day, one decomposition
A198772: Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= y

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A198772.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A198772.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #representation #quadratic #graph #threejs #webGL

One day, one decomposition
A198772: Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= y

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A198772.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A198772.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #representation #quadratic #graph #threejs #webGL

One day, one decomposition
A094619: Fundamental discriminants of real quadratic number fields with class number 2

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A094619.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A094619.html

#decompwlj #maths #mathematics #OEIS #javascript #php #3D #numbers #graph #threejs #webGL #fundamental #discriminants #real #quadratic #number #fields #class

One day, one decomposition
A094619: Fundamental discriminants of real quadratic number fields with class number 2

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A094619.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A094619.html

#decompwlj #maths #mathematics #OEIS #javascript #php #3D #numbers #graph #threejs #webGL #fundamental #discriminants #real #quadratic #number #fields #class

Flattening Bézier Curves and Arcs
https://minus-ze.ro/posts/flattening-bezier-curves-and-arcs/
#ycombinator #graphics #vector_graphics #flattening #approximation #Bézier #quadratic #cubic #elliptical #arcs #blossom #De_Casteljau #subdivision #arc_length #path_length

Flattening Bézier Curves and Arcs
https://minus-ze.ro/posts/flattening-bezier-curves-and-arcs/
#ycombinator #graphics #vector_graphics #flattening #approximation #Bézier #quadratic #cubic #elliptical #arcs #blossom #De_Casteljau #subdivision #arc_length #path_length

#Processing #python #py5 #quadratic

#Processing #python #py5 #quadratic

I have some thoughts I'm attempting to write up WRT that quadratic paper (1) shared by @fatlimey. But anyway since probably most peeps seeing this are interested in single precision results....handling that case (if you can promote to doubles) is almost no work (2) at all. (Of course it's all moot if spurious over/underflows aren't a concern)

1) https://mastodon.gamedev.place/@fatlimey/110584284601341773

2) https://gist.github.com/Marc-B-Reynolds/7dee8803d22532e12d2a973c16a33897

#FloatingPoint #quadratic

I have some thoughts I'm attempting to write up WRT that quadratic paper (1) shared by @fatlimey. But anyway since probably most peeps seeing this are interested in single precision results....handling that case (if you can promote to doubles) is almost no work (2) at all. (Of course it's all moot if spurious over/underflows aren't a concern)

1) https://mastodon.gamedev.place/@fatlimey/110584284601341773

2) https://gist.github.com/Marc-B-Reynolds/7dee8803d22532e12d2a973c16a33897

#FloatingPoint #quadratic

Once again I solve a #cubic #equation using the famous method. I explain a little bit how to solve the equation, and then switch to #python to solve the #quadratic equation, and then print all 3 solutions.

https://qr.ae/prmQES

What I find interesting is: b^2 -4ac > 0 can be rewritten to say that the arithmetic mean of roots is > geometric mean. But what even IS geometric mean for two complex numbers?

#math #mathematics #quadratic #equations

What I find interesting is: b^2 -4ac > 0 can be rewritten to say that the arithmetic mean of roots is > geometric mean. But what even IS geometric mean for two complex numbers?

#math #mathematics #quadratic #equations

This plane represents all possible #quadratic #equations with real coefficients.

The area in red is where both roots are real because the discriminant b^2 - 4ac is > 0. All the quadratics with imaginary roots lie inside the white region that's a parabola itself.

Interesting.

#maths

This plane represents all possible #quadratic #equations with real coefficients.

The area in red is where both roots are real because the discriminant b^2 - 4ac is > 0. All the quadratics with imaginary roots lie inside the white region that's a parabola itself.

Interesting.

#maths

Finally the most sophisticated of the three is Simpson’s rule in which pairs of adjacent strips use a #quadratic #parabola to interpolate between the ordinates. This even better at convergence than the trapezium rule. I’ve shown a different function here because for the function shown above the difference between the approximation and the numerical #approximation is not discernible.

#MyWork #Mathematics #Maths #Numerics #SimpsonsRule #FreeSoftware #CCBYSA #Wikipedia #Wikimedia

Got sick of not having a #calculator that can #solve #quadratic #equations, so I made one. In #Rust!

https://gist.github.com/mcb2003/6f6779fce0af8bd9881b63636a280f3f

I was explaining to my wife yesterday how #DifferentialCalculus gives us a way to find the #gradient of a #function at any point and to illustrate it I wrote a short routine in #Maxima to draw the #tangent to any point on a graph of a function. Here we see the example for the #quadratic and #reciprocal functions, x^2 and 1/x i.e. a #parabola and a #hyperbola respectively.

#MyWork #Gif #AnimatedGif #CCBYSA #WxMaxima #Mathematics #Maths #Calculus #Differentiation

The Quadratic Equation Solution a Few Thousand Years in the Making - Everyone learns (and some readers maybe still remember) the quadratic formula. It’s a pillar of alge... more: https://hackaday.com/2020/01/03/the-quadratic-equation-solution-a-few-thousand-years-in-the-making/ #polynomial #mischacks #quadratic #featured #math