imatfaal

As Sriman has pointed out the Part 2 means that the original triangle is either isosceles (with BC as base) or equilateral - thus AE is the same point as AD; this seems correct to me from a quick glance and scribble. This would also mean that there is no (as there can be no) triangle AED - exactly as you say; the internal angles of any triangle AED would have to be over 180 degrees as both angles AED and EDA would be right-angles. OK - first Idea 1. If Median AD is the same as Altitude AE then line AD and line AE are the same and points D and E are at same point on line BC (side a). 2. If (1) is true then triangle is either isosceles with side a as base or equilateral. 3. Therefore length b=c and angle B=C 4. We know for a triangle to exist any two sides must be longer than the third 5. As we know triangle ABC exists then : a<b+c, b<c+a, c<a+b 6. As we are told that triangle made up of sides a^2,b^2,c^2 has an area (and thus exists as a triangle) we all know a^2<b^2+c^2, b^2<c^2+a^2, c^2<a^2+b^2 7. From 3 and 6 we know that a^2<2b^2 8. The Cosine rule states that a^2=b^2+c^2-2bcCosA 9. From 3 and 8 we know that a^2=b^2+b^2-2b^2CosA = 2b^2-2b^2CosA 10. Rearrange this to CosA= (a^2-2b^2)/(-2b^2) 11. From 7 and 10 we know that both numerator and denominator must be negative - thus CosA is positive 12. If Cos A is positive then A lies between 0 and 90 degrees 13. We know from 2 that angles B and C must be less than 90 degrees ( if equilateral then angles = 60 degrees; if isosceles then angles <90) 14. We can show that A is less than 90, and B and C are less than 90 - triangle is an acute triangle. Just noticed that 5 is not necessary. Hope this is right Both statements are necessary and sufficient to tell that ABC is acute triangle and neither statement on its own would be sufficient (3)

If it is logically complete and internally consistent - it must be able to represent itself recursively and thus factors such as Godel come into play. The universe includes all those mathematical complex systems which we can show to be either incomplete or logical inconsistent (or sometimes both but never neither) - how can something complete and consistent be both the container and the constituent of something that is incomplete and inconsistent? Or is this a "logically consistent and logically complete" computational system which does not allow for mathematics; if you bandy about terms such as logically consistent but deny mathematic interrogation of that consistency then it begins to sound as if you were merely reaching for buzzwords rather than making a solid arguable contention.

I have never really seen infinitesimals used formally - are they the same as when a physicist talks about epsilon where epsilon is of arbitrary smallness ie a tiny addition / subtraction way smaller than the main variable

! Moderator Note moved to Speculations. Please take a moment to read the rules and guidelines to that forum Thanks

Trolling is pretty poor form - and members will remember it and assume that you are continuing. And I presume you realise that the quote about tact wasn't Isaac Newton but some advertising dude in America? Asking Sir Isaac about tact would be as useful as asking him about who is gonna win next years X-Factor! Sir Isaac Newton was renowned as a fairly nasty and vindictive man who collected enemies, fostered dislike, and seeminly delighted in vitriol

! Moderator Note We are not great fans of bumping! And from my perspective it seems that this is a perfect speculations thread - it is against the mainstream ideas in science, but you are making a valiant effort to defend your corner and show the worth of your idea.

Well there is a tiny bit of multiplication

Great set of posts. Thanks to all so far in this thread - really good stuff.

The altitude of a triangle divides the angle and forms a perpendicular to the side opposite the angle; ie D must lie on BC (side opposite A) and line AD must be perpendicular to line BC * * I think for the other two side/angles of a right triangle the altitude is the same as the side itself - but for the hypoteneuse / right angle this is not the case

You will note that your final factorization places a 9 on the outside of the brackets - ie your answer is divisible by nine. The digital root of a number that is divisible by nine is always nine (and vice versa) This was known back with the ancients (some of these techniques were in Liber Abaci - by Leonardo Bonacci; much of this "new to Europe" technology was from India and Arabia). I think the ancient Indian mathematicians could well have known of this idea - they definitely knew of very closely related ideas.

That's one line and general - dunno what new formula you might be referring. Perhaps you could stop being so elliptic and ask in a more straight forward manner

If you got 18 I would be impressed - if you got 19 in you were cheating and squeezing them in. I very much doubt it is NP complete; it does not smell as if it would reduce to the other NP-C problems. And even if it were it would not necessarily be solvable in exponential time (if all NP-C needed exponential time then P would definintely not equal NP and I would claim my million pounds). I reckon 13 or 14 ish... Whilst the rest of the family dozes off the vast amount of food I prepared earlier we are a pigs in blankets rather than devils on horseback sort of family - I might do a bit of modeling to see if I can get past a dozen

probably wouldn't have needed a big one - from his memoirs he was such a small sickly baby that he fit in a two-pint pot!

Not sure if this is short enough for you

Don's spoil Christmas by looking at sill database servers (I am just waiting for the roast spuds). Thanks Dave. Happy Christmas

I hadn't seen this in all the brouhaha after the election - Ok it is slightly pious and maybe not worth a hill o' beans in the longterm; however, it is still worthy of applause and a great sentiment upon which to base future decisions. http://sfbos.org/sites/default/files/r0484-16.pdf

There seems to be no predictive power in your ideas - they are just description. Could you explain, for instance, how your theory would allow us to calculate the radius of a geostationary orbit? You say spacetime is a loose soup of elementary particles - how does it bend? We have a theory that predicts quantitatively (not in a broad brush stroke prose like yours) why black holes form - why should we jettison GR and use your idea? Etc

! Moderator Note Mike Smith Cosmos I am going to insist you stick to your own self-appointed script on this one; you made certain claims in the OP and the thread will be a discussion of those points and nothing more. I will not allow it to turn into another meaning-lite meandering blog. Re-read your OP, address the fact that members have contradicted your assertions (sometimes with counter-examples - other times more baldly), and build a focused argument. Repetition, deviation, and blather will result in the thread being locked.

So I am correct in thinking that if you can possibly know what the state is without measurement (and thus disruption of the state) then you cannot have entanglement? Ie it is that strict

Just as an aside - as the Lorentz factor works on a ratio of velocities rather than an absolute value you can use any unit for velocity you like; but of course, you are completely correct, they must be the same units for v and for c

I have been to 5 room hotels which are slower than that! Read up on Hilbert's original thought experiment - that and his list of questions are great reading even for a layman like myself. Then for a sobering afterthought read up about David Hilbert himself and the tragedy of the Mathematics department at Gottingen - the loss of one of the greatest flourishings of talent we may witness for many years.

There is a lot of spurious detail there. We only know those figures to 3 or 4 decimal places when you convert to Systeme International - mainly due to the uncertainty in the gravitational constant which we could even be wrong about the third decimal place in SI units

Frankly, using nuance as a verb means that you will be alongside me in the execution line when the firing squad assembles* *Would you accept the last cigarette along with the blindfold?

Will I be shot at dawn for suggesting that gender is a societal construct and the different outcomes to do with fertiliszation by X sperm and Y sperm is to do with determining the sex not the gender.

Am I being super-dim? Where is the chess section?