Monthly Archives: July 2020

Hasse Diagrams

Posted on July 27, 2020 by Sumant Sumant

Hasse diagrams provides us a compact way of visualizing Partially Ordered Relations. They diagrams are easy to visualize because the diagonal pairs (reflexive) are not required. Transitive edges are removed by drawing the connected graph from bottoms up.

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Basic Relations

Posted on July 27, 2020 by Sumant Sumant

The 5 main relations on which we build other relations like Equivalence and Posets are Reflexive Irreflexive Symmetric Antisymmetic Asymmetric Transitive  

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Hamiltonian Cycle Vs Eulerian Cycle

Posted on July 25, 2020 by Sumant Sumant

Here is a set of simple graphs which illustrate that one cannot predict if a given graph is Eulerian then it will imply Hamiltonian or vice a versa.

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Havel Hakimi Theorem

Posted on July 20, 2020 by Sumant Sumant

The purpose of Havel Hakimi Theorem is to find out if a given degree sequence of a graph is valid or not. Here is a visual way to see what happens in the algorithm when we delete a vertex.

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A Visual Proof of a Geometric Series

Posted on July 20, 2020 by Sumant Sumant

Here is a proof of series . I learned this proof in Visual Math by Starbird. Notice that if we add the  trapezoidal strips we can cover the whole area. The triangle in the trapezoidal strips is   the area. … Continue reading →

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Eulerian Vs Hamiltonian Circuit

Posted on July 20, 2020 by Sumant Sumant

Given a graph one can see that there is no relation between Hamiltonian and Eulerian circuits. A given graph could be both, either or none.

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Finding Square Root of a Number using Geometric Construction

Posted on July 17, 2020 by Sumant Sumant

Here is a construction to find the square root of a number using Similar Triangles. This is the same proof we use for the proof of AM GM inequality. Where instead of augmenting the segment by we augment it by … Continue reading →

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Multiplying and Dividing Numbers Geometrically

Posted on July 17, 2020 by Sumant Sumant

How can we add and multiply lengths Geometrically.  With just ruler and compass its pretty straighforward. Draw the length of the two segments such that they are making an arbitrary acute angle. Mark unit length on one of the segment … Continue reading →

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Geometrical Construction of Golden Rectangle

Posted on July 17, 2020 by Sumant Sumant

This is an easy way to construct a golden rectangle. Notice how Pythagorean identity is use to construct a side of length and added to half of the unit square length using compass.

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Lunes of Hippocretes

Posted on July 13, 2020 by Sumant Sumant

I saw this problem in Posamentier’s book and recently I found this in Starbird’s lecture. This was probably an attempt by Hippocretes to square the circle. The amazing thing is that the area of lunes is equal to the area … Continue reading →

Posted in Geometry, Math History, Proof, Symmetry | Tagged , | 1 Comment