is it true that if a knife is left in a pyramid it will never become blunt at a certain height?
823544
Yes, very true.\n\nA knife that is never used will not become blunt.
916691
The closer you get to a cube shape (i.e., width=length=height) the better.\n\n**************\n\nOoops. You're right, it's deceptive. While a cube maximizes the volume for a GIVEN area, in this problem we decrease the total area the more we cut from the sheet. So, you need to express the volume of the cube in terms of the heights of the sides.\n\nI did a quick re-calc, and decided that the squares (i.e, the height of the resulting sides) should be 1/3 m.\n\nGood question!
891467
The only pyramid I ever heard of in China was the one of the Chinese emperor that was built over a few thousand years ago. It was mounded together. They did sona grams of the mound and found that it was a huge complex  covering a few hundred acres. They were never allowed to dig tin the area. The Chinese government still fears the curse behind the mound ... That if anyone disturbs the finally resting place the country will be destroyed by the emperor after he is awaken.
554629
never. in order for it to be tanget to the circle, it needs to be outside the circle. if the vertex is on the circle, it CAN have 1 tangent with an angle of 180 degrees
953022
There sure is!  \n\nFirst, recall this: given a tetrahedron, choose any of its faces to be its base.  Now find the area of the base (remember all the faces are triangles).  Next, find the perpendicular distance from the fourth vertex of the tetrahedron to the plane that contains the base.  This distance is the height of the tetrahedron.  Now the volume of the tetrahedron is 1/3 X area of its base X its height.  \n\nNow, using three-dimensional Cartesian co-ordinates, consider the tetrahedron ABCD where A=(0,0,0), B=(27,0,0), C=(0,16,0), and D=(0,0,3).  Face ABC is a right triangle in the x-y plane.  The two perpendicular legs of ABC have lengths 16 and 27, so the area of face ABC is 1/2 X 16 X 27 = 216.  The distance of D from the x-y plane is 3, so the volume of ABCD is 1/3 X 3 X 216 = 216.  \n\nLet E=(8,2,0).  E lies in the x-y plane in the interior of ABC.  Join E to A, B, C, and D with line segments.  Triangle ABC is subdivided into triangles ABE, BCE, and ACE, and tetrahedron ABCD is subdivided into tetrahedra ABED, BCED, and ACED, and the heights of these three sub-tetrahedra are also 3.\n\nThe distance from E to the x-axis is 2, so triangle ABE has \narea = 1/2 X 2 X 27 = 27 and tetrahedron ABED has \nvolume = 1/3 X 3 X 27 = 27.  \n\nThe distance from e to the y-axis is 8, so triangle BCE has \narea = 1/2 X 8 X 16 = 64 and tetrahedron BCED has \nvolume = 1/3 X 3 X 64 = 64.  \n\nArea of ABC = 216, area of ABE = 27, and area of BCE = 64, so triangle ACE has area = 216 - 27 - 64 = 125 and tetrahedron ACED has area 1/3 X 3 X 125 = 125.  \n\nThat does it!
108420
Well I would think if it were infinite in size then you would never be able to find an edge since, it would also be infinitly high :)  I think. . .
421382
a pyramid. 3 sides and the bottom is 4 sides. but only 3 corners.
382445
Theoretically, you are correct. However small the additional weight is in one pan, the beam must rotate till it comes to vertical position.\n\nIn practice, the pivot about which the beam turns is not exactly at its center point.\n\nHowever we can make it as close as it is possible.\n\nNext is the sharpness of the pivot. Theoretically it should be a point. But with a microscope we will see it is some what blunt.\n\nAnother thing is mass distribution on both sides of the beam should be uniform. There is practical limit.\n\nBecause of these imperfections a small additional weight placed in one pan makes the moment about this small deviated point of the center equal to the moment of the less weight placed in the other pan.\n\nThis is called sensitivity of the balance. By careful manufacturing process we increase this accuracy.\n\nKeep a foot scale on your index finger and balance it. Since the finger has some width, you can easily balance it. The center of the scale can be displaced to some extent. \nBut it will be difficult to balance it on a sharp edge.  Depending upon the sharpness the sensitivity increases.\n\nIf every thing is nearly perfect the beam should oscillate about a mean position.
1005622
Having not read Ralph's question I'm just guessing here, but a stick sharpened at both ends presents a problem in that a stick is at best a crude weapon/tool and being sharp on both ends makes it a treacherous weapon/tool.
807585
when u shave a hair you end up blunting off the tip down near the root.  The natural shape of a hair is tapered.  By cutting it close to the root you then eliminate this tapering and end up with a thicker, blunter tip as the hair then grows back out.  So yes, it may appear thicker now but over time will taper back to a lesser thickness as the hair is worn back to a more natural tapering.
654251
No, because the charges will have to distribute to opposite sides of the strip (as if it was a loop rather than a mobius strip), however since we are dealing with a one dimensional object (essentially), the charges cannot do this.
218075
The wedge works like two inclined planes. A wedge is like a nail, have you ever tries to hit the nail in the tip and drive the head through the wood? it would be much harder wouldn´t it.
55013
There are many pyramids. They are mostly made of rock; some have dirt fillings.  You need to be more specific to get a better answer.
1059138
Well, I'm sure that those pyramids really exist. There are many argumenst and facts which support tesis of Sam Osmanagic about existing huge and accient pyramids in Bosnia.\nThey researching the hills using the hightech methodology, as linear and termal inercing satelite photos which show us that the the hills are not natural.\nThe are 5 pyramids at the valley called as "Valley of bosnian pyramids" and all of them have correctly orientated geometrycal sides at East, west south and north. Three main pyramids making completly correct trinangle. And nature can't to that,\nThere are also many underground ways under the pyramids. Radar analysis shows  that. During exavcations found the block, huge blocks of pyramids in all four sides of every pyramids.\nMany archeologists do not accept Sam Osmanagic's theory, but, no one of them did't came here to see that.\nAly Barakt - egiptian geologist, who all his life working on reseraching and discovering the pyramids also said that he is sure that Bosnia has many pyramids. Momentaly, he and many other archeologists, geologists working on the excavations the bosnian pyramids, inclouding one of the most known egiptian archeologist dr. Lamiya....
214806
If the magnet was not strong enough to actually magnetize the knife blade, then no harm has been done.  If the knife blade does have a magnetic field on it, then it can possibly pick up very small particles of iron when it is used.  These are very small iron filings.  They may be almost too small to see with just the naked eyeball (without using a magnifying glass).\n\nIf the blade is used with iron filings on the blade, it will tend to become dull faster than if it is used without these.  As long as the blade is occasionally and carefully wiped with an oiled rag, this will remove the iron and no harm will be done.
753315
I agree with you - if you want the light to shine through, leaves small spaces in between.\n\nBut do you really need the light?  If you look, pyramids are solid and brown, with no light coming out of them.\nhttp://images.google.com/images?client=firefox-a&rls=org.mozilla:en-US:official_s&hl=en&q=pyramids&btnG=Google+Search&ie=UTF-8&oe=UTF-8&sa=N&tab=wi \n\nI suggest you cover the sugar cubes with the sand (maybe it'll stick better if you put glue on the sugar cubes), but I'm not so sure about the light idea
1027706
It is said Confucius would not allow knives at his table as it could be an act of aggession and this lead to the spread of chopsticks.  An all out ban on knives I have not been able to locate any info on