#### The Four Colour Mapping Theorem

How many different colors are sufficient to color the countrieson a map in such a way that no two adjacent countries have thesame color? The figure below shows a typical arrangement ofcoloured regions. Notice that we define adjacent regions as those...

https://astarmathsandphysics.com/university-maths-notes/topology/2389-the-four-colour-mapping-theorem.html#### Collisionjs in Mid Air

Particles will collide if they are in the same place at the same time. Particles that collide in mid air, subject only to the force of gravity will be moving as projectiles, and the simplest typ of collision that can take place is between particles...

https://astarmathsandphysics.com/a-level-maths-notes/m1/3553-collisionjs-in-mid-air.html#### Cartesian Form of a Plane From the Vector Form

A common form for the equation of a plane is the Cartesian form \[ax+by+cz=d\] . We can deduce the Cartesian form of a plane from the vector form \[\vec{r}(s,t)=\vec{r}_0 + s \vec{u}+t \vec{v}\] where \[\vec{s}, \: \vec{t}\] are twop vectors in the...

https://astarmathsandphysics.com/ib-maths-notes/vectors-lines-and-planes/4899-cartesian-form-of-a-plane-from-the-vector-form.html#### More Advanced SUVAT Questions

Not all suvat questions can be solved with a single application of the suvat formulae. Sometimes two applications are required, simultaneous equations are formed and these must be solved. A particle starts from rest at a point O. It accelerates...

https://astarmathsandphysics.com/a-level-maths-notes/m1/3570-more-advanced-suvat-questions.html#### The Meaning of Phrases Used in SUVAT Questions

SUVAT questions involve using the five equations To answer a SUVAT question you need three of the quantities s, u, v, a or t. Often however the values of some of these quantities is hidden behind phrases used in the question. Typical phrases and their...

https://astarmathsandphysics.com/a-level-maths-notes/m1/3588-the-meaning-of-phrases-used-in-suvat-questions.html#### A Brief History of the Elements

The ancient Greeks 2,000 years ago thought there were only four elements – earth, air, fire and water. Chemistry was a very primitive affair, since experimental physics was unknown. Instead scientists came to conclusions using reason and deduction....

https://astarmathsandphysics.com/igcse-physics-notes/368-a-brief-history-of-the-elements.html#### A Brief History of the Elements

The ancient Greeks 2,000 years ago thought there were only four elements – earth, air, fire and water. Chemistry was a very primitive affair, since experimental physics was unknown. Instead scientists came to conclusions using reason and deduction....

https://astarmathsandphysics.com/gcse-physics-notes/696-a-brief-history-of-the-elements.html#### Using Matrices in Cryptography

Cryptography hiding and uncovering information in codes. Whenever information is required to be sent from one place to another so that even if it were intercepted it would still be secure, it must first be put in the form of some code. When it is...

https://astarmathsandphysics.com/ib-maths-notes/matrices/1011-using-matrices-in-cryptography.html#### Definitions

Terms commonly used everyday by ordinary people may have a slightly different meaning in physics. Many people for example confuse velocity and speed. These are not the same, the difference being that velocity is the speed of a body in a certain...

https://astarmathsandphysics.com/ib-physics-notes/mechanics/1356-definitions.html

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