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Interesting Aspects of Platonic Solids

Platonic solids are five. They are the essential basis for all other solid Geometry. The 5 platonic solids are polyhedra with regular polygon faces. The faces and vertices are identical. They are referred as perfectly symmetrical polyhedra. Each platonic solid obeys their relationship # of faces+ # of vertices=  # of edges+2(Euler).If a solid has to be a platonic solid, the figure  must use the same regular polygon for all its faces and have the  same number of faces  meet at each of its vertices.

The platonic solids and their regularities were originally discovered by Pythagoreans and they were called the Pythagorean solids. They were later named by the Greek Philosopher Plato who wrote about them in detail in his book ‘Timaeus’.

The Tetrahedron

The Tetrahedron is bounded by four equilateral triangles. The number of vertices is three. The number of polygons meeting at a vertex is three. The number of faces for tetrahedron is four.  The number of edges of the tetrahedron is six. The number of vertices of the tetrahedron is four.

The Hexahedron

The hexahedron is a platonic solid. It is bounded by 6 squares. The number of vertices is four. The number of polygons meeting at vertex is three. The number of faces is six. The number of edges of the hexahedron is twelve. The number of vertices for hexahedron is eight.

The Octahedron

Octahedron is a platonic solid. It is bounded by eight equilateral triangles. The number of vertices is three. The number of edges is twelve. The number of polygons meeting at a vertex is four. The number of faces for an octahedron is eight. The number of vertices of the octahedron is six.

The Dodecahedron

The dodecahedron is a platonic solid. It is bounded by twelve equilateral pentagons. The number of vertices is five. The number of polygons meeting at a vertex is three. The number of edges of a dodecahedron is thirty. The number of vertices is twenty. The number of faces is twelve.

The Icosahedron

The Icosahedron is a platonic solid. It is bounded by twenty equilateral triangles. The number of vertices is three. The number of polygons meeting at a vertex is five. The number of faces is twenty. The number of edges of the icosahedron is thirty. The number of vertices is twelve.

Geometry is an interesting learning, if you have interactive methods to learn it. Geometry tutors online make it all the more fun for you to learn with their practical examples for you to follow. To know more about platonic Solids, chat with a live Geometry tutor online and get more interesting details about the topic.

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9 Math Hacks That Will Change Your Lives

Mathematics still proves to be among the most horrifying subjects that kids encounter. But with a bunch of simple mathematical tricks, children can pull of mathematics hastily and smoothly. There are too many of them. However for now, we will see 9 of them making student life easier with little bit of math homework help.

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Today we will be seeing how to make use of basic arithmetic operators such as division, multiplication, addition, and subtraction, to master the art of dealing two or more numbers with ease. In most cases, they prove to be useful as we deal with these operators in our day to day life every now and then. Let us not wait anymore and jump to our discussion.

Multiplying any 2 digit number with 11

Let us say we want the result for 52 multiplied by 11.

We will add up both numbers and put in between.

If in case the two digits add up to give another two digit number then keeping the second digit intact we will carry forward the first digit to add up to the first digit of the original number.

Multiplying any 2 digit number ending with 5 with itself

With this method, you can get the square of any 2 digit number ending with 5.

Let us say we want square of 25.

We will multiply first digit with its successor digit and put 25 towards the end. That’s it!

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Multiplying n-digit number with 5

Sometimes it can be a real big deal to multiply large numbers. However, in this method we multiply large numbers with 5 instantly to get result.

For this, just divide the number by 2. If remainder if zero, put zero to the division result. If remainder is anything other than zero, simply put 5 to the division result.

Multiplying any number by 4

It is a very simple trick wherein instead of multiplying by 4 directly, you multiply that number with 2 twice.

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Calculating % of any number

First multiply the top two numbers and then put decimal two places away from the last digit.

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Multiplying 2 large numbers

When you have to multiply two large numbers, try to round it off in multiples of 10, 100, 1000… and so on. Then cross multiply and add.

Dividing any number by 5

It is highly simple. Just multiply the number by 2 and move decimal one place away from last.

Subtracting any number from 1000

Subtract all digits individually from 9 except for the last digit that you subtract by 10.

General multiplication rules

Distribute multiplication into addition and subtraction operators to make things easier.

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Summing up…

An expert online math tutor can help kids out with far more innovative techniques then we just saw. Every expression in mathematics has a secret technique with which it can be solved easily and rapidly. However, it comes from loads of practice that only online math tutoring can help you out with. Mathematics is full of numbers, operators, expressions, equations, formulas, concepts, and what not. What we just saw is how you can create magic using the basic arithmetic operators. In our future articles we will be focusing more on how you can create magic with other mathematical concepts used in day to day life. Even you can suggest us techniques that you know, which we will feature in our future articles. Just leave your comments and let us know what you think about our comprehensive article.

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How To Sort And Solve Elapsed Time Story Problems

Time is what keeps all of us going every single day. Did you ever wonder what would have happened if we did not have a unit to measure time? Life would have got really complicated as we cannot keep track of any activity that has been done. Luckily, for most of us we learn how to measure time from a very young age starting childhood, we know the seconds, minutes and hours. To get even further we have the days, months and the years. All these are the most basic units for measuring time.

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Now that we are familiar with the units to measure time let’s take a look into how we can apply them in math word problems. Time always has a story to tell, but most students find it difficult to understand and solve when there is a word problem asking for the elapsed time. Here are some very useful tips and solved practice questions that will not only help you to understand questions related to elapsed time but also make you realize how simple they are:

Like any story even in the word problems we have a start time where the question begins and the end time where the question ends and in-between lies the time elapsed which has to be sorted out or solved for.

Now, let’s solve few word problems.

Jeremy likes to play soccer he goes for soccer practice every single day. He reached the playground around 5:00 PM and finished his practice at 6:00 PM. Calculate how long did Jeremy practice soccer on the playground?

Here in this question we are given that Jeremy reached the playground at 5:00 PM. (This is the start time.)

Later, we are given Jeremy finishes his practice around 6:00 PM (This is the end time.)

Now for calculating the time elapsed we need to find the difference between the end time and the start time. Hence we have

As shown above, this gives us the time elapsed for Jeremy soccer practice is 1 hour.

This question was quite simple as we have the time difference of just one hour. Now let us take a look at a question, where there is a time difference of more than an hour.

Let’s modify the same question:

Jeremy starts from home for his Soccer practice at 4:30 PM and returns home around 6:30 PM. Find the total time spend by Jeremy to reach back home after his soccer practice?

Here Jeremy leaves home for soccer practice at 4:30 PM and reaches the playground at 5:00 PM. The time taken can be calculated by the difference as shown in the diagram below.

We already calculated from the previous question, that Jeremy spent 1 hour at the soccer practice, this implies he leaves the playground at 6:00 PM and reaches home at 6:30 PM. This can be calculated as show below:

Finally, let’s bring it all together in one step as show in the diagram below:

We get, the total time spent by Jeremy to return back home equals 30 minutes + 1 hour + 30 minutes =2 hours.

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This is the kind of approach you may want to apply for any given word problem on elapsed time. Break the given time interval into hours and minutes, later find the total sum. Let us look at one more example:

Haley went camping with her family, they reached the campsite at 3:45 PM and took 1 hour 15 minutes to make all the arrangements. What time did they finish all the arrangements?

Here divide the time interval into hours and minutes as shown in the diagram below.

Hence it took around 5:00 PM for Haley and her family to make all the arrangements at the campsite.

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Why to dig a little deeper while studying algebra?

Algebra is a branch of mathematics that contains equations, numbers and letters to find out the exact figure of something. As it contains variable and constant figures to solve the equation, most students find it difficult to solve their homework problems, and as a result, they need extra help with algebra homework. Before learning and doing their assignments, students should know the importance of this subject.

 Here are a few important aspects:

• Apart from the use in engineering or research field, it is applied by the professionals like computer scientists, architects, electricians and lots more.
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• Practicing algebra actually makes one smarter and helps to build better IQ.
• If one wants to extend life changing help to mankind, then also it is necessary to learn Algebra properly.

Apart from academic life, Algebra is a part of real life too

You will be absolutely wrong if you think that algebra will be of no use in real life. If you think that after completing the academic part, it’s time to say ‘good bye’ to Algebra, you are completely wrong. You should take the move today by doing more practice and homework assignments, and whenever you need effective help with algebra homework, it is available online anytime, anywhere and for everyone.