Monday, August 31, 2009

What is a Tesselation in Geometry

From geometry terms and definitions ,a tessellation is created when a shape is repeated over and over again covering a plane with out any gaps or overlaps.Another word for a tessellation is "Tiling".
A tessellate means to form or arrange a small square in a checkered or mosaic pattern.
A regular polygon has 3/4/5 or more sides and angles,all equal.

In other words,A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher. Tessellations are seen throughout art history, from ancient architecture to modern art.Let's see some examples from 10 grade math geometry

A regular tessellation means a tessellation made up of congruent regular polygons .i.e
with all sides of same length and congruent means polygons of same size.We can get the Volume with out using formula for volume by using Tessellations.




You can draw Tessellations for any polygon ,say Hexagon,Octagon...etc.

Thursday, August 20, 2009

equation properties along with examples

In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra.
In the left-hand side of the above equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the results added after wards. Because these give the same final answer (8), we say that multiplication by 2 distributes over addition of 1 and 3. Since we could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers distributes over addition of real numbers.


Let's a example problem from 7th grade math equations

Solve for x

-4(2-3x)=7-2(x-3)

by using distributive law

Answer:-

Let's have a look at the answer from algebra answers

-4(2-3x)=7-2(x-3)

-8+12x=7-2x+6

-8+12x=13-2x
+8 +8
---------------
12x=21-2x
+2x +2x
----------------
14x=21

x= 21/14

= 3/2

is the answer.

Similarly we have associative property of addition ,which helps on addition of
different equations,

Thursday, August 13, 2009

Subtraction with regrouping

This subtraction help explain how to subtract different types of numbers
Start subtracting from the ones place.

If the subtrahend is lesser than minuend in ones place then we borrow 1 from tens place.

If the subtrahend is lesser than minuend in tens place then we borrow 1 from hundreds place

Example:
Subtraction with regrouping


1.Start from the ones place, 4 is lesser than 6. So 1 is borrowed from 2 and 4 becomes 14.

2.In tens place, 2 becomes 1, now again 1 is less than 5, so 1 is borrowed from 8 and 1 becomes 11.

3.In ones place 4 is subtracted from 7.

Answer: 368


For more help on this ,you can reply me.