Archived May, 2026.

Fun with 3D!

mark

(10 points)

We studied some fun equations in class the other day. We learned about planes, spheres and ellipsoids. There are limitless variations on those themes. Your task for this assignment is to just play around and find something you like.

So... to that end, fire up Desmos 3D, and play around. Try and find something that seems kinda interesting to you. Once you do, you should respond to this post with

Your function nicely typeset and
A graph of your function.

I'll help you in class but you can read more about this in these two Meta posts:

n read more about how to use the site in these other meta posts:

Also, if you really need some inspiration, check out Desmos's 3D Gallery.

❤️ 6

mark

audrey

My equation is x^2 + y^2 - 3z^2 = 9 and it looks like

❤️ 3👍 2

User 018

This is my function:
5x\cos x^{2}+\sin x+y^{3}\sin y^{3}=4\tan z^{7}+30

This is what that looks like:

❤️ 3👍 2

User 012

Fun with 3D

My equation is

333(x^{14}+y^3)-80(z^6)=40

and it looks like this!

❤️ 3👍 2

User 020

My equation is:

x^2+y^2+z^2+\cos^2(6z)=4

and it looks like this:

❤️ 3👍 2

audrey

My equation is x^2+2y^2-3z^2=9. It looks like so:

👍 2❤️ 1

User 033

My equation is x^4+2y^7+9z^4=278
Looks like a cowboy hat:

👍 2❤️ 1

User 022

My equation is 2-3x^2+9y^2+3z^2=3 it looks like 2 inverse cones connected in the shape of a funnel

👍 2❤️ 1

User 004

My function is:
cos^2(x)+y^2+z^2=0.5
It looks like this:

👍 3❤️ 1

User 009

I made an equation that, when repeated, looks like a book!
z = (x+n)^3 + y^2 + z
Where 0.1 \le n \le 1 repeated many times.

👍 2❤️ 1

User 032

My function is

\sin x^2 + y^4 + \sqrt{\tan \pi} \, z^2 = \frac{\tan 3}{\cot 5}

❤️ 2👍 1

User 025

My equation is -x^2+(5y+3)^2+4z^2=5

👍 2❤️ 1

User 001

My first graph I thought was cool was this sombrero.

👍 1❤️ 1

User 039

\cos{((y + z)} / {x^3}) = 1

👍 2❤️ 1

User 048

X^5+8y^2+15z^4-3y^4=4

It looks horses saddle Lego piece

👍 2❤️ 1

User 041

My equation is

x^{16} + 2 y^{16} - z^{24} = 10

And it looks like this!

👍 2❤️ 1

User 006

Hot dog from Saturn with equations:

👍 1

User 023

My function is: \sin x-\sin y+\cos z=0

👍 2❤️ 1

User 035

My function is:

6y^{2}-5x^{4}-10x^{3}+3y^{2}

It looks like this:

👍 2❤️ 1

User 028

x^3+y^5/7+z^7=3

👍 2❤️ 1

User 007

My equation is \cos\left(x^{2}-4y^{3}+534y\right)

👍 2❤️ 1

User 049

My function is: x^2 + y^{50} + z^2 = 25

Here is my image:

👍 2❤️ 1

User 046

This is my function:

\frac{\sin x}{6}+\sqrt{5\cos y}=\frac{\tan z^{x}}{\tan y}

This is what that looks like:

👍 2❤️ 1

User 008

My function is y^3 + x^2 \cos(\sin x) = z^3 \sin x
and this is what it looks like!

👍 2❤️ 1

User 016

My equation was
\sin^2 x + \sin^2 y - \cos^2 z = \tan 3
and it looks like this:

👍 3❤️ 1

User 002

My equation is (\cos(2xz))25y^2+25z^3=36.
This is what it looks like

👍 2❤️ 1

User 026

My equation is

\sum_{n=1}^{10} \left( x^{2} \right) + \sin\left( y^{2} \right) + \left( z^{2} \right) = 16

It looks like this

👍 2❤️ 1

User 034

my equation is:
sin x + tan y + tan 3z = 10
and it looks like this:

I like how is begins to seemingly phase out

👍 2❤️ 1

User 010

My equation is:

\Bigl(\, (4+(\sin2\pi v)(\sin2\pi u))\sin3\pi v,\; (\sin2\pi v)(\cos2\pi u)+8v-4,\; (4+(\sin2\pi v)(\sin2\pi u))\cos3\pi v \,\Bigr)

It looks like:

👍 1❤️ 1

User 042

Thought that this weird "X" shape was interesting.

x^2 + y^2 + z^2 = 3x^2 - 6y^{45}

👍 2❤️ 1

User 037

My equation is z= sin(x) +cos(y) it looks like this:

👍 2❤️ 1

User 024

\sin(x)+\cos(y)

👍 2❤️ 1

User 044

My equation is \frac{2}{7}x+\left(y^{-2}+\frac{3}{10}\right)+\left(z+1\right)^{-1}=2 and it looks like this

👍 2❤️ 1

User 021

My equation is \sqrt{\tan\left(z\right)\tan\left(x\right)\tan\left(y\right)}-e^{y^{2}}=67

Confetti! Hooray!

👍 2❤️ 1

User 015

My equation is x^{2}-y^{3}+z^{4}-\sin 6x+\sin 7y-\sin 8z=a and it looks like this:

👍 2❤️ 1

User 027

Here's my function:

\cos(y)\,x^{2} + \cos(x)\,y^{2} + 100 z^{4} = 4

It looks like this:

👍 2❤️ 2

User 050

My equation is x^{4}+10y^{2}\cos z=0
and it looks like this:

👍 2❤️ 1

User 040

The equation I chose to use here is x^3y^3z^3=x+y+z. Here is what it looks like:

👍 2❤️ 1

User 031

2x^{2}-\frac{1}{9}y^{2}z^{2}=6

👍 2❤️ 1

User 017

I made a fun little hat, though its technically a few functions.

I used the following functions to form my hat:

x^2+y^2+4z^2=4

x^2+y^2+(3z-2)^2=2

x^2+y^2+((9/4)z-3)^2=1

x^2+y^2+((3/2)z-3)^2=1/3

x^2+y^2+(z-(8/3))^2=1/9

👍 2❤️ 2

User 003

My equation is: x^{2}+y^{2}+z^{2}+\sin5x+\sin8x+\sin5x-z-x-y=a

👍 1❤️ 1

User 013

my equation is: (\cos(9x/3y))(y^{-7})(z^{3}) = 1 and looks like

👍 2❤️ 1

User 011

My attempt at creating a tesseract: these are my two formulas:

Orange cube:

\frac{1}{7}\left(x^{9}+y^{9}+z^{9}\right)-\left(2x^{8}+2y^{8}+2z^{8}\right)+10=0

Blue cube:

\frac{1}{2}\left(x^{6}+y^{6}+z^{6}\right)-8\left(2x^{2}+2y^{2}+2z^{2}\right)+64=0

👍 3❤️ 1

User 019

My equation is x^{1}/a^{3}+y^{4}/b^{2}+z^{2}/c^{2} = 5 . Here's what it looks like:

👍 2❤️ 1

User 036

The equation I used is this:

\mathbf{r}(u,v) = \left(\left(6 + \left(\sin(6\pi v)\right) \left(\sin(6\pi u)\right)\right) \sin(6\pi v),\right.
\left.\sin(6\pi v) \left(\cos(6^6\pi u)\right) + 6v - 6,\right.
\left.\left(6 + \left(\sin(6\pi v)\right) \left(\sin(6\pi u)\right)\right) \cos(\pi v)\right)

👍 3❤️ 1

mark

Hey @User 051, I love your picture! Do you think you could typeset your formulae using the forum's techniques?

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User 043

My equation is:

\sin\pi x - 3y^{2} + \cos\left(2z\right) = 1

It looks like:

👍 3❤️ 2

User 038

This is my equation: x^{2} + y^{2} + z^{2} + \tan 4x + \tan 8y + \tan 4z = a.
It looks like this:

👍 2❤️ 1

User 029

My equation is:
\left(2x-2\right)^{2}-\left(3y-9\right)^{2}+\left(z-290\right)^{3}=6^{2}

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mark

@User 052 Could you wrap dollar signs around you math to get it to typeset?

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User 029

thank you for helping me fix that.

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User 030

My function is z=4eysin(2x-5):

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