# Number

## Farewell 2021 with 3n+1

The Youtube algorithm one day pushed a video "The Simplest Math Problem No One Can Solve - Collatz Conjecture" to me. After viewing the video, I thought that my VRMath2 could easily visualise the 3n+1 graph with its LOGO programing. I am happy that my VRMath2 application is still working after almost three years in low maintenance mode. With some simple coding. I have written a LOGO program that can take a number (natural number) and the turtle will draw its 3n+1 graph. The 3n+1 problem is simple. It starts with a natural number; if the number is odd, multiply it by 3 then add one; if the number is even, the number is divided by 2. These rules apply until the resulting number is one. It is interesting that it seems any given natural number will end with 1 after applying the 3n+1 rules, but how?

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## Newton's cradle twist

**R**ecently, there is discussion about pendulum wave effect produced using the Newton's cradle. There are many YouTube videos about pendulum waves. Having seen some of these "amazing" wave effect, I thought that VRMath2 Editor should be able to produce a fake, but good enough to show the effect of pendulum wave simulation. And here you go, see the 3D simulation below.

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## LITHIUM 9D

## Animated Atomic Model

Here is my first attempt at a transforming model, I found it useful to give the centre a texture to conceptualise what was "spinning". I have not yet worked out how to roll up and tilt right at the same time (moving both axis').

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## Christmas scene

**W**hat do you imagine for Christmas? Although Christmas is in summer time in Australia, I can still picture a snowy scene of white Christmas. There are snowflakes falling down from the sky. The ground is white in daytime and gray in the night. Trees could be green if not covered by snow. There is a snowman sitting on the ground, and some Christmas music....

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## Resizable Christmas tree

**T**his is a simple Christmas tree consists of a cone and a cyliner. In order to create multiple trees with different sizes, I have included an input into the tree procedure.

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