Hegemony

[archimage_a]

They also got pwned.

[Nero]

Does that mean Rocco is your alt, Dusty?

I smoke too much to be afraid of fire.

[Nero]

[Retech]

Heh... (did this because I got bored)

 

Assume line AC is a diameter. Now please prove that Shape ABCD is a rectangle

EDIT: To clear something up that was a question on a math test of mine a couple months back.

 

Do we have to prove it from the ground up, or can we use the pythagorean theorem and the stuff about cyclic quadrilaterals?

[Grim_]

Heh... (did this because I got bored)

 

Assume line AC is a diameter. Now please prove that Shape ABCD is a rectangle

EDIT: To clear something up that was a question on a math test of mine a couple months back.

 

Do we have to prove it from the ground up, or can we use the pythagorean theorem and the stuff about cyclic quadrilaterals?

you can use the pythagorean theorm and pretty much all of the theories that you know

[Nero]

Just write down 'It looks like a rectangle, therefore it is a rectangle'. If they dispute it ask the teacher what they think a rectangle looks like.

[archimage_a]

Can we prove it is not a rectangle.

 

*Clears throat*

What Rectangle?

[Retech]

If you draw the radius to point d, you get two isoceles triangles. We can call the center of the triangle O. Then we have triangles AOD and COD as isoceles triangles, so we can say the base angles of AOD are x and the base angles of COD are y. Then we have 2x+2y (adding the angles that form the angles of triangle ACD) equaling 180. Then divide by two to get x+y = 90.

 

Then we notice that the angle D is made of x+y, so therefore angle D is equal to 90. By triangle congruence, Angle B is also 90 degrees. Then we can simply draw the other diameter DB, and we can do the same thing, noting that they are also 90 degrees.

 

Problem solved. :P

 

YAY MATH!

[Grim_]

If you draw the radius to point d, you get two isoceles triangles. We can call the center of the triangle O. Then we have triangles AOD and COD as isoceles triangles, so we can say the base angles of AOD are x and the base angles of COD are y. Then we have 2x+2y (adding the angles that form the angles of triangle ACD) equaling 180. Then divide by two to get x+y = 90.

 

Then we notice that the angle D is made of x+y, so therefore angle D is equal to 90. By triangle congruence, Angle B is also 90 degrees. Then we can simply draw the other diameter DB, and we can do the same thing, noting that they are also 90 degrees.

 

Problem solved. :P

 

YAY MATH!

Cough inscribed angles Cough

[Retech]

The inscribed angles theorem is not a proof, imo. I've been taught always to prove things from the basics, cough. My answer would've been worth extra credit. :P

[archimage_a]

Euclid Said So ¹

 

[hide]Definition 1.

Any rectangular parallelogram is said to be contained by the two straight lines containing the right angle.

 

Definition 2

And in any parallelogrammic area let any one whatever of the parallelograms about its diameter with the two complements be called a gnomon.

 

Propositions

 

Proposition 1.

If there are two straight lines, and one of them is cut into any number of segments whatever, then the rectangle contained by the two straight lines equals the sum of the rectangles contained by the uncut straight line and each of the segments.

 

Proposition 2.

If a straight line is cut at random, then the sum of the rectangles contained by the whole and each of the segments equals the square on the whole.

 

Proposition 3.

If a straight line is cut at random, then the rectangle contained by the whole and one of the segments equals the sum of the rectangle contained by the segments and the square on the aforesaid segment.

 

Proposition 4.

If a straight line is cut at random, the square on the whole equals the squares on the segments plus twice the rectangle contained by the segments.

 

Proposition 5.

If a straight line is cut into equal and unequal segments, then the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section equals the square on the half.

 

Proposition 6.

If a straight line is bisected and a straight line is added to it in a straight line, then the rectangle contained by the whole with the added straight line and the added straight line together with the square on the half equals the square on the straight line made up of the half and the added straight line.

 

Proposition 7.

If a straight line is cut at random, then the sum of the square on the whole and that on one of the segments equals twice the rectangle contained by the whole and the said segment plus the square on the remaining segment.

 

Proposition 8.

If a straight line is cut at random, then four times the rectangle contained by the whole and one of the segments plus the square on the remaining segment equals the square described on the whole and the aforesaid segment as on one straight line.

 

Proposition 9.

If a straight line is cut into equal and unequal segments, then the sum of the squares on the unequal segments of the whole is double the sum of the square on the half and the square on the straight line between the points of section.

 

Proposition 10.

If a straight line is bisected, and a straight line is added to it in a straight line, then the square on the whole with the added straight line and the square on the added straight line both together are double the sum of the square on the half and the square described on the straight line made up of the half and the added straight line as on one straight line.

 

Proposition 11.

To cut a given straight line so that the rectangle contained by the whole and one of the segments equals the square on the remaining segment.

 

Proposition 12.

In obtuse-angled triangles the square on the side opposite the obtuse angle is greater than the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle.

 

Proposition 13.

In acute-angled triangles the square on the side opposite the acute angle is less than the sum of the squares on the sides containing the acute angle by twice the rectangle contained by one of the sides about the acute angle, namely that on which the perpendicular falls, and the straight line cut off within by the perpendicular towards the acutc angle.

 

Proposition 14.

To construct a square equal to a given rectilinear figure.

[/hide]

 

¹ Euclid. The thirteen books of Euclid's elements / translated from the text of Heiberg with introduction and commentary by Sir Thomas L. Heath. Vol.1, Books 1-5(Cambridge University Press, 1956) pages 32-33

[archimage_a]

And again, we are here.

 

India attacks Wu, taking both cities with relative easy, as well as the Pakistan-Byzantia Territory.

 

Iran begins crossing to Saudi Arabia, at the southern most tip, encountering a fleet of 35 vessels. The vessels were rocked in the water by the railgun firing Exosuits, but were easily capable of sinking a third of the attacking force before being sunk themselves. The remaining force came across a landscape filled with bunkers and artillary, eventually being entirely annhilated. The damage in that area was very limited due to the concentration of forces.

A more Northen breakthrough was more succesful, piercing the weakly defended outer shell and invading the cremey nougat core of Turkey.

 

In South Africa, something rather unexpected happened...South Africa attacked! The 2 million strong army, along with 1 million strong defenders, rallied into a crushing victory over the Byzantian Hoard, buoyed up by Indian Blockade Assistance of over 100 ships, which helped to destroy Russian and Byzantian reinforcements, though some still got through, the delay made it a beach landing, turning the reinforcement into an amphibous assault. The assault then turned into a retreat as the boats scrambled to get units out of there, only to be met by the Indian fleet in a pincer like movement.

It was, at this point, something else unexpected happened, Argentinan planes began flying overhead. At first they were greeted with joy, both sides believing that their saviours had come...then they noticed the planes were dropping atom bombs.

Over 150 atom bombs were dropped, decimating the remaining 1.8 million South African forces, as well as the surviours of the DOOMED Russian-Byzantian invasion force.

 

The belegered South Africans then were called to march across Africa to engage the Argentinians, who were landing on the West Coast. Sufficing to say the South African forces were barely able to stem the tide, let alone turn the invaders back into the sea.

 

Elsewhere Argentinans invaded Carribean territories, taking them for themselves.

 

 

 

Russia

Cost of Attack: 90,000,000,000

Treasury: 502,867,651,000

 

Argentina

Cost of Attack:87,500,000,000

Second Cost of Attack: 13,500,000,000

Sub-Total: 915,972,800,000

Third Cost of Attack: 150,000,000,000

Total: 765,972,800,000

 

Byzantia

Cost of Attack: 63,000,000,000

Cost of Defence: 7,500,000,000

Sub Total: 70,500,000,000

Second Cost of Defence: 17,500,000,000

Third Cost of Defence: 90,000,000,000

Subtotal: 52,457,024,000

Fourth Cost of Defence: 7,200,000,000

Treasury: 45,257,024,000

 

South Africa

Cost of Attack: 180,000,000,000

Cost of Defence: 30,000,000,000

Total: 210,000,000,000

Treasury: 305,661,568,000

 

India

Cost of Attack: 68,000,000,000

Treasury: 926,636,425,000

 

Iran:

Cost of Attack: 182,525,000,000

Cost of Defence: 60,000,000,000

Total: 242,525,000,000

Treasury: 867,932,478,260

 

Egypt

Cost: 78,500,000,000

Treasury: 417,558,025,600

[Grim_]

Dungeonal keep your hands off of Martinique and Guadalupe...

[Wisp]

If any non-european troop touches Italian land, or anyone attacks me and all, we'll declare war etc.

[Guest Mrmegakirby]

This war is beautiful.

 

Similarily to the previous war, I'm now selling battleships, stealth bombers, battlestations and fighter jets.

[Nero]

Very interesting. It costs over a trillion dollars to launch 8 nukes to destroy 2 little domes made out of glass, but costs only 150b to launch 150 atom bombs to destroy two armies spread across half a continent. Hm.

[Grim_]

The rules about tonnage. Simply put you used 8 atom bombs that were I believe 150x more powerful than the ones dungeonal used.

[Nero]

No the problem was that Arch classified a dome of glass as a city and decided to say I shot off 150kt nukes when I never agreed to that.

 

But it's alright, now that we can just use a zillion atom bombs to annihilate everyone I'll just do that from now on :thumbsup:

 

Oh and Wu isn't even really my land, it's just a vassal state. That being said, it did have an army of like 2m, so how many casualties did Icu take?

[archimage_a]

None, Wu decided to go pacifist after some softly-softly diplomacy from the UN. That and creating a Vassel State with a 2 million strong army which you don't have to pay for...is a bit rich...

[Guest Mrmegakirby]

Wait, why did dusty bomb retech in the first place? I just realised I was missing that piece of information :S

[Nero]

None, Wu decided to go pacifist after some softly-softly diplomacy from the UN. That and creating a Vassel State with a 2 million strong army which you don't have to pay for...is a bit rich...

...

 

This just in, Iran goes pacifist and surrenders!

 

--

 

Wu had an IAG of like...600b. I got 100b of that. So...me losing out on 500b in exchange for an army of 2m I don't have to pay for (keep in mind that NO ONE has to pay for their army) is...rich? K.

 

Wait, why did dusty bomb retech in the first place? I just realised I was missing that piece of information :S

He had the entire moon to himself; seemed a bit unfair to me.

[archimage_a]

Wu had an IAG of like...600b. I got 100b of that. So...me losing out on 500b in exchange for an army of 2m I don't have to pay for (keep in mind that NO ONE has to pay for their army) is...rich? K.

 

Yes.

Glad we cleared that up.

[Nero]

Wu had an IAG of like...600b. I got 100b of that. So...me losing out on 500b in exchange for an army of 2m I don't have to pay for (keep in mind that NO ONE has to pay for their army) is...rich? K.

 

Yes.

Glad we cleared that up.

Kk, fine. Since Wu had been a part of my country all that time without me knowing, I have a surplus of 1.5 tril + whatever I had before.

 

Cheers Arch :)

[archimage_a]

Hmmm, that doesn't work, since IAG resets every decade, so, at best, you have 500 billion extra...But since you screwed about with vassel this and vassel that, despite me saying I didn't like the idea...and the fact that it was 350 billion for 4 cities, so it would be 175 billion for 2 cities....you get nothing.

[Nero]

Glad we cleared that up :)

 

With its massive treasury boost, the ERE launches 500 1kt atom bombs into India's most populous cities.