Gaurish Korpal

Gaurish Korpal

PhD Candidate

Posts by Tags

Edwin Hewitt

Erdos

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

algorithm

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

amd

analysis

android

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

arithmetic

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

asus

bertrand's postulate

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

bicylinder

c

calculus II

chebyshev

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

chromebook

coloring

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

combinatorics

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

computations

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

computer science

conjecture

conway

counting

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

crostini

dnf

doodling

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

engineering

fedora

figures

geogebra

geometry

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

graph theory

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

graphs

grid

hp mini

hyperreal

inkscape

intel

knuth

latex

lenovo

linux

linux mint

logic

magma

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

manas ranjan sahoo

Space filling curve

4 minute read

Published:

In this post I would like to share my old writeup about there existence of a continuous surjective map from $\mathbb{R}$ to $\mathbb{R}^2$. In other words, we will prove that that Hilbert’s Curve is a continuous surjective map. The proof presented here was explained by Dr. Manas Ranjan Sahoo, 3 years ago on 15th April 2016.

matplotlib

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

matthew scroggs

metric spaces

Space filling curve

4 minute read

Published:

In this post I would like to share my old writeup about there existence of a continuous surjective map from $\mathbb{R}$ to $\mathbb{R}^2$. In other words, we will prove that that Hilbert’s Curve is a continuous surjective map. The proof presented here was explained by Dr. Manas Ranjan Sahoo, 3 years ago on 15th April 2016.

mir

mpmath

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

my research

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

non-standard analysis

number theory

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

numix

numpy

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

online

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

open-source

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

openSUSE

papers

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

pc

pdf

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

pentium

pfgplots

philosophy

piskunov

plots

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

prime numbers

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

problem solving

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

Spot The Flaw

less than 1 minute read

Published:

Many of you must have seen numerous examples of such situations where we get an absurd result and have to spot flaw in proof.

problem-solving

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

Cross Diagonal Cover - III

1 minute read

Published:

I found many counterexamples to my conjecture, like

  • for Case 2 in 7 by 5 grid we have 12, 11 by 5 grid we have 19 and 15 by 5 grid we have 26 filled squares
  • for Case 3 in 4 by 10 grid we have 10 filled squares

Also, grant93jr made the following comment:

Cross Diagonal Cover - I

1 minute read

Published:

While doodling in my college classes, I designed an algorithm which I called Cross Diagonal Cover Algorithm:

Hello World

less than 1 minute read

Published:

Here is my first post.

programming

proof

python

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

racket

rclone

reading

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

red hat

richert

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

ryzen

sagemath

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

script

Cross Diagonal Cover - V

1 minute read

Published:

This has been an exciting week! Prof. Sukanta Pati proved an interesting theorem that enables us to get decomposition of $2m-1\times n$ grids into simpler grids, hence simplifying counting to large extent (note that $m=n$ is also allowed). It enables us to surpass the difficulty posed by “more than two crosses in one square”, thus supporting the idea of colouring (i.e. not giving importance to two crosses in a square).

Cross Diagonal Cover - IV

5 minute read

Published:

While discussing this problem with Dr. Shailesh Shirali, he commented that there has to be a way to phrase the problem in terms of a ray of light being reflected off the walls of the rectangle, bouncing around, proceeding from one corner to some other corner.

security

sierpinski

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

solution

sum of primes

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

surface area

sympy

Higher Arithmetic Computations

14 minute read

Published:

In this post I discuss the options available for doing computational experiments in advanced number theory.

tablet

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

terminal-emulator

thinkpad

tikz

tikzcd

topology

Space filling curve

4 minute read

Published:

In this post I would like to share my old writeup about there existence of a continuous surjective map from $\mathbb{R}$ to $\mathbb{R}^2$. In other words, we will prove that that Hilbert’s Curve is a continuous surjective map. The proof presented here was explained by Dr. Manas Ranjan Sahoo, 3 years ago on 15th April 2016.

turner

Richert Theorem

2 minute read

Published:

In 1852, Chebyshev proved the Bertrand’s postulate:

ubuntu

vector graphics

vim

vim plug

vimrc

vimtex

wacom

writing

Reading and annotating papers

3 minute read

Published:

Following is the comparison of tech specs of my new tablet (USD 315 + taxes) with the older tablet (USD 280 + taxes):

xfce

xfce4-terminal