1.is an angular measurement in a spherical coordinate system. The vector from an observer to a point of interest is projected perpendicularly onto a reference plane; the angle between the projected vector and the reference vector on the reference plane is called the azimuth.

2.Euclid was a greek mathemetician, Also called the father of geometry ,Euclidian distance is the ordinary distance between two points.

3.Pythagorean theorem is a mathematics related to Eucludian geometry among the three sides of a right triangle, In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two sides that meet at a right angle. The equation is a2xb2=c2 which is often called the pythagorena equation.

4.Map algebra is a simple and an elegant set based algebra for manipulating geographic data, in arc gis map algebra is used to preform operations using objects,actions and qualifiers.

5.The 7 key functions of a spatial analysist consist of,

Derive new information from existing data
Apply Spatial Analyst tools to create useful information—for example, derive distance from points, polylines, or polygons; calculate population density from measured quantities at certain points; reclassify existing data into suitability classes; or create slope, aspect, or hillshade outputs from elevation data.

Find suitable locations
Find areas that are the most suitable for particular objectives (for example, siting a new building, or analyzing high risk areas for flooding or landslides) by combining layers of information. Based on a set of input criteria (for example, where areas of vacant land with the least steep terrain that are nearest to roads would be most suitable), areas in green in the graphic below are the most suitable locations for building; areas in red are least suitable. Areas in yellow are of medium suitability.

Identify the best path between locations
Identify the best path or optimum corridors for roads, pipelines or animal migration. Factor in economic, environmental, and other criteria.

Perform distance and cost-of-travel analyses
Create Euclidean distance surfaces to understand the straight-line distance from one location to another, or create cost-weighted distance surfaces to understand the cost of getting from one location to another based on a set of input criteria you specify

Perform statistical analysis based on the local environment, small neighborhoods, or predetermined zones
Perform calculations on a per-cell basis between multiple rasters, such as calculating the mean crop yield over a 10-year period. Study the neighborhood by calculating, for example, the variety of species in a neighborhood. Determine the mean value in each zone, such as the mean elevation per forest zone.

Interpolate data values for a study area based on samples
Measure phenomenon at strategically dispersed sample locations, and predict values for all other locations by interpolating data values. For instance, create raster surfaces from elevation, pollution or noise sample points.

Clean up a variety of data for further analysis or display
Clean up raster datasets that contain data that is erroneous or irrelevant to the analysis at hand or is more detailed than you need.