Geometry and Discrete Math Links

In summary, the conversation is about someone looking for links to briefly explain the laws of geometry and discrete math, specifically the Properties of Circles. They mention finding MathWorld but not being able to find the section on properties of circles. Another person suggests that a tangent drawn from two points of intersection of overlapping circles will bisect the common external tangent.
  • #1
dekoi
Would anyone happen to have some links which briefly explain some of the laws in geometry and/or discrete math? At the moment, i am looking for a summary of the Properties of Circles .

Thank you for being as helpful as you always are.


--
ps
I found MathWorld, although i can not find properties of circles section. :confused: link
 
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  • #2
No one?

bump!
 
  • #4
What are some general rules regarding a tangent which lies on two points; these two points are each on a different (sized circle), and the two circles are overlapping each other (intersecting at two points).
 
  • #5
The only one I know of (though there may be more) is that the chord drawn from the two points of intersection of the circles bisects the common external tangent.

Hope that helps! :)
 
  • #6
So if the two points of intersection are connected, and are extended to meet the common tangent, the tangent will be bisected?
 
  • #7
Yes, that's correct.
 

What is the difference between geometry and discrete math?

Geometry is a branch of mathematics that deals with the study of shapes, sizes, and properties of figures in space. Discrete math, on the other hand, is a branch of mathematics that deals with finite or countable sets and focuses on the study of discrete structures such as graphs, networks, and algorithms.

How are geometry and discrete math related?

Geometry and discrete math are both branches of mathematics that deal with different types of objects and structures. However, they are closely related as many concepts in discrete math, such as networks and graphs, can be visualized and represented using geometric figures. Additionally, many problems in geometry can be solved using principles and techniques from discrete math.

What are some real-world applications of geometry and discrete math?

Geometry and discrete math have numerous real-world applications in fields such as computer science, engineering, physics, and even art and design. Some examples include using graph theory to analyze social networks, using geometric principles to design buildings and structures, and using discrete algorithms to optimize transportation routes.

How can I improve my understanding of geometry and discrete math?

One way to improve your understanding of geometry and discrete math is to practice solving problems and exercises. You can also read books and articles on the subject, attend lectures or workshops, and work on projects that require the application of these concepts. Additionally, seeking help from a tutor or joining a study group can also be beneficial.

What are some key principles and theorems in geometry and discrete math?

Some key principles and theorems in geometry include the Pythagorean theorem, Euclidean geometry, and transformational geometry. In discrete math, some important principles and theorems include graph theory, combinatorics, and Boolean logic. These concepts are fundamental for understanding more complex problems and applications in both fields.

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