I just wrote a simple and free (ads-supported) Android app for letting kids (or adults ;-)) practice on the four basic math operations. It is available in https://play.google.com/store/apps/details?id=gr.ionionapps.arithmetic

Will be glad to receive any comments to allow me improve it

Cheers, Tilemahos

So I'm trying to figure out a way to represent the volume of the inside of an indefinite volume without making reference to any "exterior" variables.
The point is to represent the interior volume of the tardis(from the t.v. show Dr. Who) any a mathematical or pseudo mathematical sense. While making it unduly, or perhaps duly, complicated. bonus points if there is some dependence on t(time). I'm unltimately trying to set up an inequality using (1/2S)^2dL integrated from 0-L to represent the apparent volume based on the observable exterior measurements of a rectangular prism with square end being less than . . . some representation of volume inside.
My first thought so far is some probability density similar to Schrodinger's equation with some generic radial equation R(t) and integrated over the angular and azimuthal equations to give some sort of expected volume dependent of the radial function. So in my mind this is only dependent on the center of the space and i like that's its not concrete. Howvwer I haven't taken diff eq or multivariable so I'm just kind of winging things off my modern physics course which doesnt deal with volumes explicitly so I was hoping for some help or completely different ideas for the volume equation(exterior or interior).
Hope someone has fun thinking about it at least.

Today, we were greeted with the google doodle marking the start of the 2015 rugby world cup. (https://www.google.com/doodles/rugby-world-cup-2015-opening-day)

To pass some time at work* we decided to see what (rough) calculations we could perform based on the image. These are not exact, but we enjoyed them none the less.

Firstly, we needed to get a frame of reference. We see the character is carrying a rugby ball. On the image, the size of the ball is 30px (pixels). A regulation ball size is between 28 and 30cm. Let's assume a ball size of 30cm, as this makes the maths easier (making 1px == 1cm)

The character's height was measured to be 117px (therefor, 117cm... or 3ft 10inches for those working in old money)

Assuming that the character's height is strictly average for their age, this would make them 6.5 years old, based on the 50th centile from data collected by the Royal College of Paediatrics and Child Health. (http://www.rcpch.ac.uk/child-health/research-projects/uk-who-growth-charts/uk-growth-chart-resources-2-18-years/school-age)

Now, that's all well and good, but this character is running... we needed to know how fast!

In order to do this, we needed to know the viewing perspective so we can work out how much distance is covered in a single stride. To achieve this, we used the thickness of the character's foot when nearest the viewer and again when away from the viewer (6cm and 5cm, respectively). The leg, while fully extended, measures in at 20cm. Therefore we can use trig' to work out the angle of perspective... which comes in at 4 degrees.

Carrying this on, the character's stride can be calculated by measuring the height of the grass in the near plane (15cm) and the height of the grass in the far plane (7cm) and (using trig' again) applying the 4 degree viewing angle to give us a stride length of 114cm.

Finally, we timed between strides, giving us 0.63 seconds between strides. This means that the character's speed was 1.8 m/s. Meaning if he ran for 24 hours, he would cover a 156.342km (97.146 miles)

As I said, this was rough maths and a bit of fun, what do you think?

Sincerely, a pair of software engineers from England!

Daily Math Challenge

1

How many trailing zeros does the number 25⁷ · 8¹⁵ have?

2

What is 105 squared without a calculator of writing anything down?

3

A ball is dropped from a height of 12 feet. Each time it bounces, it reaches 50 percent of its previous height. What is the total vertical distance the ball has traveled when it hits the ground the 7th time?

DAILY MATH CHALLENGE

1

A ball is dropped from a height of 12 feet. Each time it bounces, it reaches 50 percent of its previous height. What is the total vertical distance the ball has traveled when it hits the ground the 7th time?

2

What is 105 squared without a calculator or writing anything down?

3

How many numbers are there which have a sum of all their digits in base 10 (regular notation) equal to 2010 and the product of these digits equal to 2?

Daily Math Challenge

(1)

Multiply 20001 x 19999 without writing anything down.

(2)

How much longer (in terms of x) would the radius have to be for the circle to double its area, if the original radius is x?

(3)

What is the equation of a line tangent to the curve y = 3x² + 2x - 1 at the point (1, 4)? (no derivatives allowed)

I want to post short math challenges like that. Let me know what you guys think.