PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (236)
Orphanage
Unclass'd (1)
Unproven (541)
Corrections (47)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Copyright
About
Owner confidence rating: Very high Entry average rating: Very high
geometry (Topic)
euclideangeometry

"geometry" is owned by rspuzio. [ full author list (11) | owner history (2) ]
(view preamble | get metadata)

View style:

See Also: finite projective plane, projective plane, point-free geometry, comparison of common geometries

Other names:  Egyptian geometry
Also defines:  Greek geometry, Euclidean geometry
Keywords:  calculus

Attachments:
non-Euclidean geometry (Definition) by Wkbj79
Euclidean geometry of plane (Topic) by matte
differential geometry (Topic) by rspuzio
Euclidean geometry of space (Topic) by pahio
analytic geometry (Topic) by pahio
axiomatic geometry (Topic) by CWoo
geometry as the study of invariants under certain transformations (Topic) by rspuzio
Log in to rate this entry.
(view current ratings)

Cross-references: concepts in symplectic geometry, fundamental concepts in differential geometry, bibliography for differential geometry, classical differential geometry, PlanetMath, separation, hyperbola, quadrature, language, extrema, tangents, Fermat's method, chooses, Calculus, objects, differential geometry, index of entries on compass and straightedge constructions, topics on vectors, Euclidean geometry of space, Euclidean geometry of plane, necessary, accessible, order, sort, increasing, axiomatic, infinitesimal, non-commutative, discrete spaces, infinite-dimensional, dimensions, addition, properties, origins, pyramids, even, areas, feasible
There are 113 references to this entry.

This is version 43 of geometry, born on 2002-12-25, modified 2008-04-20.
Object id is 3824, canonical name is Geometry.
Accessed 38698 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
 51-01 (Geometry :: Instructional exposition )
Pending Errata and Addenda
None.
[ View all 4 ]
Discussion
Style: Expand: Order:
forum policy

jump to page: 1 2 3 >> of 3 (14 items)

May Ponder This by PARASHAR on 2009-05-05 04:40:38
Find all times that when viewed as

1) an analog watch, the second hand is a bisector of the angle between the minute hand and the hour hand.
2) a digital watch, the time is palindrome.
To clarify: the time should satisfy both conditions when the analog clock moves continuously, while the digital one is rounded to the nearest second and shows the time in hh:mm:ss format.
[ reply | up ]
December Ponder This by PARASHAR on 2008-12-01 23:33:44
Consider a random walk on the 2-d integer lattice starting at (0,0). From a lattice point (i,j) the walk moves to one of the four points (i-1, j), (i+1, j), (i, j-1) or (i, j+1) with equal probability. The walk continues until four different points (including (0,0)) have been visited. These four points will form one of the five tetrominoes (considering mirror images to be the same). For each tetromino find
the probability that it will be the one formed in this way.
[ reply | up ]
September Ponder This by PARASHAR on 2008-09-08 19:52:08
Consider a 13x13 checkerboard. It can be partitioned into a collection of smaller square checkerboards in various ways. For example into 169 1x1 checkerboards or into 1 12x12 and 25 1x1 checkerboards. What is the minimum number of smaller square checkerboards that a 13x13 checkerboard can be partitioned into? Show how this can be done.
[ reply | up ]
Triangle by PARASHAR on 2008-09-02 20:33:34
There is a triangle with with vertices s1, s2 and s3. s1, s2 and s3 have co-ordinates (x1,y1), (x2,y2) and (x3,y3) respectively. d23 is the distance between s2 and s3. similarly d13 is that between s1 and s3, d12 between s1 and s2.

Known entities: x2, y2, x3, y3, d23
Unknown entities: x1, y1, d12, d13

A sound wave signal is transmitted from s1 and it reaches at different times at s2 and s3. We only know the time difference between wave reaching at s2 and s3.

We need to find out x1 and y1. Sound speed is 340 m/s

You can assume any values for known entities to find out the solution.

Use any method but when trying to find the solution if you could consider the generic approach it would be better means your solution should be valid if there are more s’s (s1, s2, s3, s4 ….sn)
[ reply | up ]
August Ponder This by PARASHAR on 2008-08-04 23:41:18
This puzzle is a variant of the famous 8-queens problem (see http://en.wikipedia.org/wiki/Eight_queens).

The original problem is to place as many queens as possible on an 8x8 chess board such that no queen will threaten another (a queen threatens all the squares in its row, column, and both diagonals).

In our version we need to place as many queens as possible on an NxN board, such that each queen will threaten at most *one* other queen. We ask to prove an upper bound and give a solution matching it for the standard 8x8 board as well as for a 30x30 board. The solution should be sent as pairs of x,y coordinates.
[ reply | up ]

jump to page: 1 2 3 >> of 3 (14 items)

Interact
post | correct | update request | add example | add (any)