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How to calculate the volume of a flatbottomed, corked bottle, partially filled with a fluid having only the ruler as a measuring tool?
The 3D graphics made by me and presented below gives an answer to this question. 

08 Jan 2016, 20:45 

MHajduk wrote: How to calculate the volume of a flatbottomed, corked bottle, partially filled with a fluid having only the ruler as a measuring tool? 

09 Jan 2016, 04:00 

hi MHajduk,
what software you use to made that 3D bottles? 

09 Jan 2016, 04:53 

YONG wrote: How about the case when there is only a very small amount of fluid? When the fluid can't even completely fill up the noncylindrical portion of the bottle, what should we do? take a can with precisely known volume, fill it completely with a fluid with far less density than water (because almost empty, corked bottle may not sink in water)  it can be ethanol, kerosene or something like that  put carefully the bottle inside  it will sink and displace amount of the fluid that will be equal to the outer volume of the bottle. Take the bottle off and measure amount of the fluid that left in the can. Difference between the initial and final amounts will give us the outer volume of the bottle. It wouldn't be precise but always... 

09 Jan 2016, 11:16 

sleepsleep wrote: hi MHajduk, 

09 Jan 2016, 11:22 

MHajduk wrote:


10 Jan 2016, 03:01 

Just so it in a social network: _2016 = 666+666+666+(6+6+6)


10 Jan 2016, 18:54 

idle wrote: Just so it in a social network: _2016 = 666+666+666+(6+6+6) 

10 Jan 2016, 20:19 

In case you are interested in drawing circles with a huge diameter (by "huge" I mean here really big ones, measured in kilometers or so) there is a tricky idea needed because the ropeandthestick method won't work for circles with a diameter bigger than several dozen meters. Here you can use a method based on the well known fact from geometry stating that all angles inscribed in a circle and subtended by the same chord (lying on the same side of the chord) are equal.


14 Jan 2016, 23:54 

"Still life with vases", 3D graphics.


17 Jan 2016, 22:56 

Prove the following inequality:


19 Jan 2016, 08:49 

19 Jan 2016, 17:58 

impressive vase!


20 Jan 2016, 06:15 

like the vase too!
cycles engine? MHajduk? 

20 Jan 2016, 19:47 

shoorick wrote: impressive vase! sleepsleep wrote: like the vase too! 

20 Jan 2016, 21:42 

the most impressive math done by MHajduk is not in his formulas.


21 Jan 2016, 01:13 

Ptolemy's theorem: A convex quadrilateral can be inscribed in a circle if and only if the product of the lengths of one pair of opposite sides added to the product of the lengths of the other pair is equal to the product of the lengths of the diagonals. Thus, in a cyclic quadrilateral ABCD we have
AB*DC + AD*BC = AC*BD 

21 Jan 2016, 01:35 

tthsqe wrote: the most impressive math done by MHajduk is not in his formulas. 

21 Jan 2016, 09:51 

perfect blender!


21 Jan 2016, 18:57 

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