Exactly 3 out of n propositional variables is allowed to be true
Is it of this kind?
At least 3 out of n propositional variables is allowed to be true
At most 3 out of n propositional variables is allowed to be true
Exactly 3 out of n propositional variables is allowed to be true
At least 3 out of n propositional variables is allowed to be true
At most 3 out of n propositional variables is allowed to be true
BlinkerSpawn wrote:More generally, functions that equal their n-th derivative will be composed of terms of the form Ce^kx, where C is a constant and k is an n-th root of unity.
gameoflifemaniac wrote:BlinkerSpawn wrote:More generally, functions that equal their n-th derivative will be composed of terms of the form Ce^kx, where C is a constant and k is an n-th root of unity.
So, that n-th root can be complex?
gameoflifemaniac wrote:BlinkerSpawn wrote:More generally, functions that equal their n-th derivative will be composed of terms of the form Ce^kx, where C is a constant and k is an n-th root of unity.
So, that n-th root can be complex?
Macbi wrote:Yes, in particular cos(x) = (1/2)e^(ix)+(1/2)e^(-ix) and sin(x) = (-i/2)e^(ix)+(i/2)e^(-ix).
muzik wrote:What would the tilings {1,∞} and {∞,1} look like?
[o]ther convenient ‘magic’ like using symmetries, transferring results via isomorphisms, homotopy equivalence or elementary equivalence (Urban’s Ultraviolence Axiom) is done by theorem proving, not the foundations.
Apple Bottom wrote:(Ultraviolence? Ultraviolence? Or just autocorrect gone wild?)
Bullet51 wrote:Apple Bottom wrote:(Ultraviolence? Ultraviolence? Or just autocorrect gone wild?)
It may be "univalence".
Well, autocorrect has gone wild.
gameoflifemaniac wrote:What curve has the property that an object rolling on it has constant speed?
77topaz wrote:gameoflifemaniac wrote:What curve has the property that an object rolling on it has constant speed?
Assuming there's no friction, simply a horizontal surface.
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
77topaz wrote:gameoflifemaniac wrote:What curve has the property that an object rolling on it has constant speed?
Assuming there's no friction, simply a horizontal surface.
gameoflifemaniac wrote:What curve has the property that an object rolling on it has constant speed?
gameoflifemaniac wrote:But a sphere rolling on a horizontal surface with some initial velocity will slow down. I figured out the curve will have decreasing curvature. The curve would look roughly like this:
img
But what curve is it exactly?
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
gameoflifemaniac wrote:What curve has the property that an object rolling on it has constant speed?
gameoflifemaniac wrote:But a sphere rolling on a horizontal surface with some initial velocity will slow down. I figured out the curve will have decreasing curvature.
But what curve is it exactly?
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
You'll have to give your definition more precisely. I can't think of anything that could have a property like this. If a path from A to B intersects itself at C, then there is a shorter path that goes from A to C and then directly to B. So the shortest path from A to B can't intersect itself. In most kinds of geometry the shortest path is considered straight.muzik wrote:I've probably asked this before, but is there a name for the following type of geometry, and has it been studied in any detail?:
Take two points anywhere on a plane, labelled A and B. If the straightest possible path from A to B must intersect itself at least once, the plane can be said to be "XXXX".
muzik wrote:I've probably asked this before, but is there a name for the following type of geometry, and has it been studied in any detail?:
Take two points anywhere on a plane, labelled A and B. If the straightest possible path from A to B must intersect itself at least once, the plane can be said to be "XXXX".
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner wrote:muzik wrote:Take two points anywhere on a plane, labelled A and B. If the straightest possible path from A to B must intersect itself at least once, the plane can be said to be "XXXX".
The geometry would have to be limited in directional movement, like lines tracing the paths of photons reflecting off mirrors.
x = 120, y = 114, rule = B3/S23
51bo$52b2o$54b2o$56bo$57bo$48bo8bo$49b2o7bo$51b2o6bo$10b97o$10bo42bo7b
o44bo$10bo42bo6b2o44bo$10bo41b2o5bo46bo$10bo40bo5b2o47bo$10bo39bo5bo
49bo$10bo38bo5bo50bo$10bo37bo5bo51bo$10bo42b2o51bo$10bo95bo$10bo48b2o
45bo$10bo48bobo44bo$10bo48b2o45bo$10bo48bobo44bo$10bo48b2o45bo$10bo95b
o$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo
95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$
10bo95bo$o9bo95bo$bo8bo10b2o83bo$2bo7bo8b2o85bo$3bo6bo8bo86bo$4bo5bo8b
o86bo$4bo5bo7bo87bo$5b2o3bo6bo9b3o76bo$7b2obo5bo10bobo76bo$9b2o4bo11b
3o76b4o$10bo4bo11bobo76bo3bo$10b2o3bo11bobo60b2o13b2o4bo$10bobobo75bob
o11bobo5b2o$10bo2b2o75b2o11bo2bo7bo$10bo79bobo8b2o3bo8bo$10bo79b2o9bo
4bo8bo$10bo89bo5bo9b2o$10bo89bo5b3o8bo$10bo88bo5b2o2bo7bo$10bo87bo5bob
o2bo8bo$10bo87bo4bo2bo2bo9bo$10bo86bo5bo2bo3bo$10bo85bo5bo3bo4bo$10bo
95bo4bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo
$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo
95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$10bo95bo$
10bo95bo$10bo95bo$10bo48b3o44bo$10bo48bobo44bo$10bo48b3o44bo$10bo48bob
o44bo$10bo48bobo44bo$10bo95bo$10bo95bo$10bo95bo$10bo53bo41bo$10bo52bo
42bo$10bo51bo43bo$10bo51bo43bo$10bo50bo44bo$10bo49bo45bo$10bo48bo46bo$
10bo48bo46bo$10bo47bo47bo$10b97o$58bo$58bo$57bo$57b2o$59bo$60bo$61b3o$
64b4o$67b2o!
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