Actually, if you look at the template for the puzzle, the area is initially perfectly filled - the guy just made bad cuts. The trick is that the L-pieces are slightly longer at their base than the narrower quadrilaterall; they have to be wedged back into the puzzle space for the second configuration which creates the extra space. The triangle at the top is a true triangle as the cut is just a straight line, so it's a slightly different illusion than the missing square puzzle.
>> ^Payback:

>> ^ForgedReality:
>> ^Payback:
Ok, I thought this was going to be an illusion... Kept waiting for the bigger piece to end up the same size as the smaller one.

Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.

Well, a bit mysterious. The total area inside the bounding box doesn't change, and the pieces fill it, so the sum of their areas would seem to be the total area of the bounding box. You shouldn't be able to "rearrange" the pieces to create a largish hole, because no matter what you do, the sum of the areas of the pieces remain constant and seemingly equal to the area inside the box. The first arrangement is obviously not perfectly filled, and the second one moves those errors to one square area.

>> ^MaxWilder:

>> ^ForgedReality:
Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.
FR, if you can't see why this shouldn't be possible, you lack a basic understanding of geometry.
The area of the square is width x height. In the first configuration, the pieces cover the full area of the square. In the second configuration, they do not. The area has not changed. The pieces have not shrunk. So why is there a part of the puzzle that is empty?
If everybody else is so dumb, please enlighten us as to how this is possible.
My only guess is that the pieces are being squished into the second configuration, and the squished portions make up for the missing coverage. But that would mean this would not work with sturdier material, or in a computer model.


It depends how you built the rigid pieces/computer model. There ARE gaps in the first configuration, they're just small and spread. The second configuration reduces the smaller, spread gaps and converts them into one larger gap.

Check that thing i linked, you'll see that the triangle in that picture isn't a true triangle, it just looks a lot like one. It's actually got 4 sides, and you can apply something similar here.

Dan Secrest - The reason why there is a gap in these "triangles" is actually related to fibonacci's sequence. But I wont go there. The easy solution is simply because those are not triangles. Each has 4 sides. The red triangle has a different slope than the green. The red triangle has slope 3/8 while the green has 2/5. Therefore, in the upper "triangle" there is increasing slope along the hypoteneus and in the lower there is decreasing. The short short answer is that the areas of both triangles are EXACTLY the same, but the lower triangle has a gap to make up for the different slope it has on the hypoteneus. If anything, these resemble non-euclidean triangles because there angles add up to over 180 degrees.>> ^dannym3141:

Notice how easily the pieces slip into place in the first layout compared to how he has to force them into place on the second layout.
It's related to this:
http://nrich.maths.org/content/01/06/six3/triangle-illusion.gif

Notice how easily the pieces slip into place in the first layout compared to how he has to force them into place on the second layout.

It's related to this:
http://nrich.maths.org/content/01/06/six3/triangle-illusion.gif

>> ^mefa:

>> ^EmptyFriend:
it's spelled realeaux triangle, if anyone was caring to look it up.

Except it's really spelled "reuleaux triangle".


doh, typo. good catch.

>> ^TheFreak:

Isn't Wankel feeling rather smug right about now.


I thought the same thing, and Wikipedia greeted me with this:

"The rotor of the Wankel engine is easily mistaken for a Reuleaux triangle but its curved sides are somewhat flatter than those of a Reuleaux triangle and so it does not have constant width. "

Source (English translation) http://translate.google.de/translate?u=http%3A%2F%2Fwww.der-wankelmotor.de%2FTechniklexikon%2Ftechniklexikon.html&sl=de&tl=en&hl=de&ie=UTF-8

I'm still partial to the reference though.

>> ^EmptyFriend:

it's spelled realeaux triangle, if anyone was caring to look it up.


Except it's really spelled "reuleaux triangle".

it's spelled realeaux triangle, if anyone was caring to look it up.

As someone with experience in the manufacture of various plastics:

AHEM. By looking on the bottom of different plastic containers, you'll notice the "recyclable" symbol made of three curved arrows forming a triangle, as well as a polymer code, such as PE, PC, HDPE, PP, PS, V, LDPE or PETE. These indicate the type of plastic used in the product. PE would be polyethylene, HDPE is High Density polyethylene, PC would be polycarbonate, PP for Polypropylene, Polystyrene, Vinyl/Poly vinyl chloride (PVC) and polyethylene terephthalate.

The polyethelylenes and PP melt at lower temperatures (300-400 F)
PS melts higher at around 450 for a good liquid form and
PC melts the highest at 560-650 or higher.

So yeah, you're sucking a lot of juice to melt these - a lot more than you can pull from a few photovoltaics, anyway.

The front looks somewhat wierd, if you ask me. Especially those triangle-shaped air intakes below the bonnet, next to the headlights.

If you look at most freeways, they gradually slope across the surface for water drainage. So no they are not perfectly flat, but the goal for people preparing subgrades is to make the surface as even as possible while maintaining the desired grade. If the surface is really even, that means there will be the minimum amount of overage on materials when it comes to asphalt. If they prepare it properly, the machine can be set at 2-3-4 inches thick and lay all day at that depth, and when they move over to the next lane, they can lay the same thickness and maintain the grade without having to adjust. That's the goal, it meets the specs of the job and doesn't cost them in overages on material....and if they are majorly over...someone screwed up.

Now....I'm pointing out flaws in this roadway because if they were to use his design and it failed miserably there would be less chance of them ever doing it again. So what's the fault in putting it in applications where it would see more extreme conditions in a lower traffic zone to get a proof of concept? Or hell even put it on a bike path or sidewalk, if it holds up superbly for a few years......move onto a military base to see how well it holds up to extreme abuse of their heavy machinery.

Just slapping it down on a highway because that would be cool is a sure fire way to kill this prospect dead in it's tracks for a long time to come. Prove it lasts, prove it provides savings, and prove it's as safe as or better than current materials under all possible road conditions. Highways may be the goal, but it isn't the first step on an unproven concept.

Personally I think if they did this on bike paths, they'd have more luck pushing it forward..because bike paths are all about the green initiative...so if they can also kick some energy savings back to the city while testing their product. No one loses there if the materials work, and if they don't.....at least it's just a bike path that needs re-surfaced.



>> ^Payback:

Most of you keep talking about how the road needs to be perfectly flat. Well, they don't. Otherwise the concrete pads of the interstates would need to be perfectly flat. These are 3x3 squares. Every video game character you play is made up of squares and triangles. A spiked ridge between the LED/P-V "pucks" would take care of any water caused splipping.
Just because you can find fault with the guy's "ultimate" roadway, a ton of the ideas could be implemented without full conversion.
How about using those LED/P-V pucks on highways to merely to show where the lanes are at night? They could "pave" the centre and shoulder areas to provide power for streetlights and not affect the traffic surface.

>> ^Payback:

Most of you keep talking about how the road needs to be perfectly flat. Well, they don't. Otherwise the concrete pads of the interstates would need to be perfectly flat. These are 3x3 squares. Every video game character you play is made up of squares and triangles. A spiked ridge between the LED/P-V "pucks" would take care of any water caused splipping.
Just because you can find fault with the guy's "ultimate" roadway, a ton of the ideas could be implemented without full conversion.
How about using those LED/P-V pucks on highways to merely to show where the lanes are at night? They could "pave" the centre and shoulder areas to provide power for streetlights and not affect the traffic surface.


You could also have dynamic road deployment and redeployment. Need to rewire your entire highways system for an evacuation? No problem, reconfigure all signage and postings to make all available roads outgoing only, now, short of the likely bottlenecks, you have doubled your outbound traffic ability. Really, the sky is the limit. Any level of smartness to the roads brings with in untold innovation. The physical problems seem very manageable and knowable, but the benefits are easily hidden and largely unrealized. The potential is mind blowing though. Solar powered streets and buildings just makes to much since not to try and make work. So much free energy in these already used places, we just need the means to effectively harvest it, and this seems like a great idea, in any final form it takes. It is worth mentioning that glass is non-crystalline. Meaning it can flex and bend over time. Look at any old house and the windows are thicker on the bottom then the top. So it can deal with gradual gradient changes, how well is a matter of engineering.

Most of you keep talking about how the road needs to be perfectly flat. Well, they don't. Otherwise the concrete pads of the interstates would need to be perfectly flat. These are 3x3 squares. Every video game character you play is made up of squares and triangles. A spiked ridge between the LED/P-V "pucks" would take care of any water caused splipping.

Just because you can find fault with the guy's "ultimate" roadway, a ton of the ideas could be implemented without full conversion.

How about using those LED/P-V pucks on highways to merely to show where the lanes are at night? They could "pave" the centre and shoulder areas to provide power for streetlights and not affect the traffic surface.

>> ^NordlichReiter:

The part where the guy got body slammed?
He never took a judo class. If you are about to get picked up, you release the grip of your legs this way the guy picking you up has all your weight.
He basically assisted in his own body slam, buy holding on.


The problem with your theory is that you're not fighting Rampage. The strength and speed with which Rampage slammed Arona gives you very little time to react and untangle your legs from the triangle.

Wow old man, spoken like a true middle-aged fanboy. = P

Of course mma standup isn't at the level of boxing. Boxing is all standup.
Mixed martial arts is every other martial art style you can think of.

If you can't see that then you're not as smart as you'd like yourself to believe, with your crabby panties-in-a-bunch attitude. =]

A boxing round is 3 mins of standup hugging.
36 mins of dancing in boxing boots like an Acme cartoon.

MMA rounds are 5 mins of defending takedowns, submissions, head kicks, leg kicks, judo throws .. and strikes.
A MMA title fight is 5 rounds. That's 25 mins of working every muscle in your body.

If you aren't able to understand that about MMA you don't even know what you're talking about. [Which is already quite apparent]

I don't think you can appreciate all the disciplines of Mixed Martial Arts because you're sitting here complaining about heavyweights and how they aren't amazing conventional boxers.

P.S. - Fedor Emelianenko lost finally. Not due to great standup but by double submission: Armbar Triangle Choke.

My point is: of course MMA standup is sloppy. You have four or five other modes of attack you have to calculate and defend against.



>> ^highdileeho:

The standup talent isn't anywhere near the level of boxing. Is all i'm going to say and if you can't see that then your not as smart as you would like people to believe, with your pompus arrogant attitude.

the reason they were throwing haymakers was because they had to fight A 10 round match, (something mma athletes are not physiclly capable of)they were completly exhausted

...if you weren't able to understand that about fighting/boxing then i really don't know why i'm wasting my time, because you don't even know what your talking about.

mma is a good sport. I can appreciate all of the disciplines, my favorite fighter is emilionenko-- i'm not spell checking that name--, and my favorite style is sambo, it's far and away the best fighting discipline.

My point is mma needs to step up it's standup game it's sloppy.