Watery Art using Maths Expression

Graphs are wonderful thing in the learning of maths.

Not only does it reflects visual symptom or trend in data collected, it displays, if allowed, beautiful images.

This is possible if you allow you maths juice to go free and create mathematical expressions to your fancy and view them on a graph.

Below I have created one.  I visual it as water rippling through a surface (on the top view).

Hope you like this maths art of mine.

NOTE: It is created using trigonometry of circulatory expression.

Here I view a water droplet going down into the centre. It then produces ripples or waves spreading outwards in a circular manner.

Imagination ....
Maths expressing ......


:-)





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Artistic Mathematical Lantern

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Have you wondered what can maths do to art?


Below is a lantern made by a mathematical expression.

With maths, you can be assured of producing wonderful images when you have the appropriate expression.


Do create some for enjoyment.


Maths is interesting.


:-)

Math Challenge 21

Some math questions are simple and can be answered easily.

See this math challenge 20 and its answer in the comment.

But a twist of the questioning will and can make it more challenging without changing the math expression.

Below is one:

Base on math challenge 20, if all unknowns CANNOT be repeated, what are they?
Again they are integers and below 10.

Enjoy the math thrill answering this.

Merry Christmas!
^.^

Square Root | An Exciting Outcome

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Everyone knows what a square root is for and what it does to a number.

But have you tried multiple square rooting ?

What do I mean?

Let's take an example.

Start with a number, say, 3.

i)  Square root this 3.
ii) You will get a number after step one.
iii) Square root this new number again.
iv) Continue the steps above and look closely at the number.

Findings: 
You will notice that the number after multiple square rootings, will give you closer and closer to or approaching the number "1".


Now let's start with another number. This time, let's choose, 0.4

After doing the same procedures, you will again notice that the answer is getting and approaching the number "1"!

Amazing isn't it?

What other wonders can you find from this Square Root maths operator?
Share with me in the comment section.

Maths is interesting.........

:D

Math Challenge 19

Math does not involve variables that we can see only.

There are the logical deduction type whereby you have to visualise and come out with an answer.

Below is one good example that I would like it to be a challenge.
(Don't be frightened by this, it is just for fun.....)

Above you will find a stack of cubic boxes. There are the blue and the yellow cubes.

Question:
What is the least quantity of blue boxes must we use in order to hold the yellow boxes in the same place?

You may present your answer and how you arrive at the answer in the comment section.

Thanks for trying. And I am waiting for that interesting mathematical deduction...

Maths Is Interesting!

Cheers :-D

Solving Maths Visually

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Maths is interesting!
There are many exciting concepts and techniques one can apply.
Read on ...

There are many ways to solve a maths question.
Normally it involves taking many steps with related sequence.

However, there are also simple ways to handle a maths problem.

One such solving method is simply through visual steps.
This has no working at all.

What do I mean?

Let's look at an example.

Example:
Determine the angle B from the diagram below. Angle A is 40 degree.

Solution:

Angle B is same as angle A = 40 degree.

There is no working at all. Just the visual determination.

Concept of this trigonometrical question in geometry:
When 2 straight lines cross and meet at an angle to each other, the angle opposite to any one is the same.

As such, angle C is also equal to angle D.

This is visual maths.

Interesting?

:-D

Simple Tricky Maths Pattern

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Maths forms interesting patterns if you care to look around.

One such example is highlighted below:

12  11  10  09  08  07  06   <== row 1  (decreasing by 1)
01  02  03  04  05  06  07   <== row 2  (increasing by 1)

If you add the numbers in row 1 to that in row 2, you will get, surprisingly, the same answer throughout!

13  13  13  13  13  13  13

Why is it so?

It is a simple trick to the unwaries, actually.

Maths is not that difficult, to start off.
The answers to the above additions seem to be accidental in having the same number.
It is actually not accidental if you think abit.

The answers were intended to be 13 to begin with.

13 = 12 + 1
13 = 11 + 2
13 = 10 + 3  ....  and so on.

Though the additions seems magical with one row in ascending mode while the other row in descending mode, it is the visual maths trick that corrupts and confuses the mind.

If your principles of mathematics is good and strong, you will break through this simple trick in no time.

To excite young minds, this is a good one to try on them.

Happy playing with maths.
Maths is interesting!

:D

Time Calculation May Not Be Easy

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Counting from 1 to 100 is normal for anyone. Just increment by 1. It's that simple.

But counting time may be another story for young math students.

Why is this so?

There is the seconds, the mintes, and the hours to handle. They differ by the umber 60.

The "carry over" through addition is the number SIX!

1 min 30 sec added by 40 sec gives .......

1 min 70 sec?

Here the 70 sec includes 60 sec + 10 sec. You need to understand that for time, 60 sec means one whole minute.
Thus, 70 sec = 60 sec + 10 sec ===> 70 sec = 1 min + 10 sec.

Therefore, 1 min 30 sec add 40 sec gives ==> 2 min 10 sec.

Compare this to adding 30 by 40. Answer = 70. No more analysis.

Time base on 1 hour = 60 min, 1 min = 60 sec concept.

To test true understanding of addition (and subtraction), time is a good gauge and tool to assess learners.

Test it on young kids today to annoy them... *#^&@!
Cheers!

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Algebra Is Useful

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There are everyday events that requires the use of algebra.

Solving simple math question with unknowns can be done easily with algebra in mind.

Take the example of the math challenge 15 given by clicking this link.

What the challenge requires is the addition of a pair of 2-digit number obtained from a 4-digit number.
The higher 2-digit number is to be added to the lower 2-digit number to obtain the centre 2-digit number.

Example:
1978

Upper 19 is added to lower 78 to produce centre 97.

In that post, you are to come out with more examples of this type of 4-digit numbers.

Use of Algebra can easily solve this cahllenge.

How?

Here it goes...

As in algebra, let's assign "letter" to each digit of this 4-digit number ==> abcd

The upper pair is then 10a + b, and
the lower pair is 10c + d.

Adding them up gives, 10a + b + 10c + d = 10b + c (this is the requirement)
==> 10a + d = 9b - 9c -----(A)

Also a + c + 1 = b ==> a = b - c - 1 -------(B)
and b + d = c + 10 ==> d = c + b + 10 ----(C)

Here, it is necessary to assume b + d >10, since otherwise negative number relation will appear.
(If you find this statement tough, never mind, and read on..)

From the above 3 equations formed, you will then be able to randomly choose numbers that fit them.

You will now appreciate the usefulness of algebra in solving this math challenge.

Enjoy!
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Mathematics Letter S

Using graph and equation, you can create wonders.

Graph does not only mean lines and curves. It can be "letter" too, as seen below.



With creativity and a bit of trying, you can have surprising images formed through graphs.

With mathematics, you are not limited to equation and solving problem. You can have fun and that makes mathematics interesting.

:-)

Geometrical Errors Can Be Exciting

The learning of geometry is to allow anyone to have an idea of correct perspective to objects.

Dimensions are important in this area. Angle of view is equally important.

Drawings of object in the fore-ground and background differs because of geometry.

When the concept of geometry is violated in drawing objects, you will get interesting outcome.

This outcome, however, is apparent only in the virtual sense and cannot be physically produced.

Example of links are quoted below:



http://anythinggorgeous.blogspot.com/2009/01/staircase-of-character.html



http://anythinggorgeous.blogspot.com/2009/01/cunning-overlapping-of-objects.html



http://anythinggorgeous.blogspot.com/2008/12/twisted-rods-or-fishy-rods.html



Geometrically deceptive objects are not easily identified, and have to be closely stared at to reveal their "wonders".

Only through learning maths and its relevant topics, you can then appreciate the importance of having done it. This is very obvious in the above few examples.

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Cranes of Number "Four"

Numbers are everywhere.

Some are obvious but some are not. They have to be discovered.

Below is one that is nicely presented.

Can you see the "number" that they form?



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Lines of Wisdom

In an earlier post, the enjoyment of knowing maths was demonstrated in its ability to form pictures.

Here is another example of playing with the trigonometry to create mathematical art.



In this piece of art, 4 graphs of various mathematical expressions were overlapped to form the result.

I name this piece of art the "Lines of Wisdom".

In the graphs, maths functions like the sine and sinh operation were used together with trigonometrical multiplication.

:D

Creating A Maths Picture

Maths can be used in many ways.

It is normally used to solve daily calculations related to work, life, etc.
It can be used to model a system to understand its performance and behaviour.

However, on the fun side, it can be used to create a picture using graph as a means.

Here in this post, a picture formed through merging trigonometry with modulation technique is shown.


What do you think this picture is about?

While creating this maths picture, a kid so happened to have a glimpse of it, and commented that it looked like the front view of an aeroplane.

For me, it seems to be the captured voice of Optimus Prime, the Transformer Autobot leader.

With maths, if you understand the underlying principles of various elementary topics, you can freely come up with any mathematical figures that you wish.

Here, I have simply used the special sinc function modulated (multiplied) by a high frequency trigonometric sine function to get this mixed result.

Using graph is one way to form picture, like the one created here.
It is fun seeing your imagination materialise through using maths and graphs as the tools.

Try it for yourself. You will enjoy maths and its fun picture creation.

:D

Curious Maths Terms

Have some fun with the terms used in maths...

1) Doing multiplication without tables ===> Doing the maths problems on the floor

2) Using integration ===> Discussing with classmates and copying relevant answers

3) Using differentiation ===> Sorting out what can be done and what can't

4) Finding partial fractions ===> allowed to complete the computation partially

5) Calculating standard deviation ===> finding out how many more marks to hit standard pass grade

Caution:
Do not take this too serious, otherwise ....... you will really have to check your standard deviation.

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Maths Game - "Reversity"

This is a maths game that I strongly recommend to anyone who like to keep their brain active.

You will find it wonderful and importantly, it is free and requires only a piece of paper and a pencil to go with it.

This activity is not new. I have seen many with deviation.

Here I will share with you the concept.

CONCEPT: The target ( a list of number from 1 to 10, or similar list) is to be produced using a set of pre-defined numbers, or a certain number only. Any mathematical operation can be utilised to achieve the target.

Example:

To produce a list of number from 0 to 10 using ALL the numbers 1, 2, 3 and 4, with any of the mathematics operators, + , -, /, x, ) ( and exponential.

Here it goes...

0 = 4 - 3 - ( 2 - 1 )
1 = (4 - 2 )/ (3 - 1 )
2 = (4 + 2¹) / 3
3 = 4¹ + 2 -3
4 = 4 x 2 - 3 - 1
5 = 4 x 2 - 3¹
6 = 4 + 2 / 1³
7 = 4 + 3 / 1²
8 = 4 x 2 / 1³
9 = 4 x 2 + 1³
10 = 4 x 2 + 3 - 1

This is a simple maths game, but it involves the application of the basic principle of mathematics to achieve the targeted number for a given set of constraints.

"Reversity" - a reversal of the mathematical procedure.

Another tougher Reversity game is to have only the number 4 used.

Any deviation can be created to generate different levels of difficulties. Explore it!

Keep your mind in reverse gear ....... ! s r e e h C (reversed)
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Number Game To Make Maths Fun

Purely studying maths as it is may tied up students mentally, not to mention the staff teaching it. How to make it interesting?

You can play games with maths. With a bit of creativity, you can create lots of fun.

I just encountered one word game initiated by a nice member at the social site BlogCatalog .

The game started with a word (has to be more than 5 letters). The next member has to continue with another word but has to start it using the last letter of the previous word. Sort of fun going especially when you see the people whacking at the comment space to participate.

Improvise this concept to maths :

Maths Game

Make use of any 3 different maths operators to generate the number 18.

Rule of the game: The last maths operator has to be the first for the next person to continue, and no numbers in the operation are to be the same.

Start: 18 ==> 40 / 2 - 5 + 3 ==> .......

Happy thinking :D

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Are The Area Of The Shapes Same?

When we look at shapes, sometimes we wonder are they of the same size or area? With basic geometric understanding, we will be in a better position to deduce the answer just by comparing the shapes in question.

Look at the pairs of shapes below (Diagram A to E), and tell whether are they of the same surface area.












Visually some pairs may look bigger or smaller.

However, knowing the concept of area and combination of shapes, we can tell that only the pair of shapes in Diagram D will be different. All rest remain, even for the last digram E.

Diagram E can be easily deduced to have the same area by pasting the curvy (upper) part to the (lower) blank curvy profile, and likewise for the other half of the shape.

Shapes are InteResTing, am I correct?

:)

An Interesting Colourful Pie Chart

Pie chart is used to generate graphical representation of data. The groups of data are gathered into angular portion within a chart rounded to look like a pie; that calls for a Pie Chart.

I was doing some analysis of data and happened to generate a pie chart that amazed me.

Below is the chart that I believed gave more than the usual presentation of data. It surprised me with its wonderful mixture of colours arranged in sectors.



To me, math is more than numbers and equations. It is art too!

Do you agree with me?

I am feeling hungry after posting this. Care for a pie?

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Amazing Remainder Checking (Divide by 9)

The number 9 is a special number when it is used as a divisor.

Why so?
It produces an amazing feature.

Divide 152 by 9.

Answer is 16 with remainder of 8.

Let's add up the digits of the original number 152.

1 + 5 + 2 = 8. The answer of "8" tallies with the remainder "8" !

This is a quick way to check for correct remainder when divided by 9.

Another example: Divide 321 by 9

Answer is 35 with remainder 6.

Quick check for remainder: 3 + 2 + 1 = 6 !

Example: Divide 4488 by 9 ==> 498 with remainder of 6.

Checking remainder: 4 + 4 + 8 + 8 = 24. Remainder = 24 ?

For this case, proceed by summing up the obtained answer (24).

2 + 4 = 6. This is the remainder!

So, if you get a number (non-one digit), just continue adding up the digits.

Point to note when using this quick check method:

• When the sum of the digits is 9 or an even multiple of 9, it means there is no remainder.


• This check is for divide by 9 only.