User:Cmglee/2011

Hello!

My interest in editing Wikipedia is in illustrating articles, so let me know if you wish some article on science, mathematics or technology illustrated.

Here is some of my work to date; click on images for more details:

United Kingdom


Continental Europe


Taiwan


Singapore


Malaysia


Template:Distance_from_Sun_using_EasyTimeline
&#9742; &isin; The following chart shows the range of distances of the planets, dwarf planets and Halley's Comet from the Sun.

Template:Hyperfocal_distance_depth_of_field_using_EasyTimeline
&#9742; &isin;

Template:Tallest_building_history_using_EasyTimeline
&#9742; &isin; Timeline of recent buildings that have held the title Tallest building in the world. Heights of buildings are to scale. Note the early buildings that lost the title as their spires collapsed.

I'm My Own Grandpa
Family tree showing how the narrator of the song is his own grandfather.

Mode (statistics)
When X has standard deviation σ = 0.25, the distribution of Y is weakly skewed. Using formulas for the log-normal distribution, we find:
 * $$\begin{array}{rlll}

\text{mean}  & = e^{\mu + \sigma^2 / 2} & = e^{0 + 0.25^2 / 2} & \approx 1.032 \\ \text{mode}  & = e^{\mu - \sigma^2}     & = e^{0 - 0.25^2}     & \approx 0.939 \\ \text{median} & = e^\mu                 & = e^0                & = 1 \end{array}$$ Indeed, the median is about one third on the way from mean to mode.

When X has a larger standard deviation, σ = 1, the distribution of Y is strongly skewed. Now
 * $$\begin{array}{rlll}

\text{mean}  & = e^{\mu + \sigma^2 / 2} & = e^{0 + 1^2 / 2} & \approx 1.649 \\ \text{mode}  & = e^{\mu - \sigma^2}     & = e^{0 - 1^2}     & \approx 0.368 \\ \text{median} & = e^\mu                 & = e^0             & = 1 \end{array}$$ Here, Pearson's rule of thumb fails.

Common logarithm
The following example uses the bar notation to calculate 0.012 &times; 0.85 = 0.0102:


 * $$\begin{array}{rll}

\text{As found above,}      &\log_{10}0.012\approx\bar{2}.079181                                                    \\ \text{Since}\;\;\log_{10}0.85&=\log_{10}(10^{-1}\times 8.5)=-1+\log_{10}8.5&\approx-1+0.929419=\bar{1}.929419\;,    \\ \log_{10}(0.012\times 0.85) &=\log_{10}0.012+\log_{10}0.85                &\approx\bar{2}.079181+\bar{1}.929419     \\ &=(-2+0.079181)+(-1+0.929419)                &=-(2+1)+(0.079181+0.929419)              \\                             &=-3+1.008600                                 &=-2+0.008600\;^*                         \\                             &\approx\log_{10}(10^{-2})+\log_{10}(1.02)    &=\log_{10}(0.01\times 1.02)              \\ &=\log_{10}(0.0102) \end{array}$$ * This step makes the mantissa between 0 and 1, so that its antilog (10mantissa) can be looked up.

Ratio of volumes of a cone, sphere and cylinder of the same radius and height
The above formulas can be used to show that the volumes of a cone, sphere and cylinder of the same radius and height are in the ratio 1 : 2 : 3, as follows.

Let the radius be r and the height be h (which is 2r for the sphere).

$$\begin{array}{llll} \text{Volume of the cone}    & = \tfrac{1}{3} \pi r^2 h & = \tfrac{1}{3} \pi r^2 (2r) & = (\tfrac{2}{3} \pi r^3) \times 1 \\ \text{Volume of the sphere}  & = \tfrac{4}{3} \pi r^3   &                             & = (\tfrac{2}{3} \pi r^3) \times 2 \\ \text{Volume of the cylinder} & = \pi r^2 h             & = \pi r^2 (2r)              & = (\tfrac{2}{3} \pi r^3) \times 3 \end{array}$$

The discovery of the 2 : 3 ratio of the volumes of the sphere and cylinder is credited to Archimedes.

Ratio of surface areas of a sphere and cylinder of the same radius and height
The above formulas can be used to show that the volumes of a sphere and cylinder of the same radius and height are in the ratio 2 : 3, as follows.

Let the radius be r and the height be h (which is 2r for the sphere).

$$\begin{array}{llll} \text{Surface area of the sphere}  & = 4 \pi r^2       &                    & = (2 \pi r^2) \times 2 \\ \text{Surface area of the cylinder} & = 2 \pi r (h + r) & = 2 \pi r (2r + r) & = (2 \pi r^2) \times 3 \end{array}$$

The discovery of this ratio is credited to Archimedes.

Subpixel rendering
For example, consider an RGB Stripe Panel:

RGBRGBRGBRGBRGBRGB            WWWWWWWWWWWWWWWWWW         R = red RGBRGBRGBRGBRGBRGB    is      WWWWWWWWWWWWWWWWWW         G = green RGBRGBRGBRGBRGBRGB perceived  WWWWWWWWWWWWWWWWWW  where  B = blue RGBRGBRGBRGBRGBRGB    as      WWWWWWWWWWWWWWWWWW         W = white RGBRGBRGBRGBRGBRGB            WWWWWWWWWWWWWWWWWW

Shown below is an example of black and white lines at the Nyquist limit, but at a slanting angle, taking advantage of Subpixel rendering to use a different phase each row:

RGB___RGB___RGB___            WWW___WWW___WWW___         R = red _GBR___GBR___GBR__    is      _WWW___WWW___WWW__         G = green __BRG___BRG___BRG_ perceived  __WWW___WWW___WWW_  where  B = blue ___RGB___RGB___RGB    as      ___WWW___WWW___WWW         _ = black ____GBR___GBR___GB            ____WWW___WWW___WW         W = white

Shown below is an example of chromatic aliasing when the traditional whole pixel Nyquist limit is exceeded:

RG__GB__BR__RG__GB            YY__CC__MM__YY__CC         R = red    Y = yellow RG__GB__BR__RG__GB    is      YY__CC__MM__YY__CC         G = green  C = cyan RG__GB__BR__RG__GB perceived  YY__CC__MM__YY__CC  where  B = blue   M = magenta RG__GB__BR__RG__GB    as      YY__CC__MM__YY__CC         _ = black RG__GB__BR__RG__GB            YY__CC__MM__YY__CC

Circuit de Monaco
Google Maps with rough circuit

Article translation

 * Federation of Malaya
 * MSC Malaysia
 * Sultan Abdul Halim ferry terminal bridge collapse