Latin1 was the early default character set for encoding documents delivered via HTTP for MIME types beginning with /text . Today, only around only 1.1% of websites on the internet use the encoding, along with some older applications. However, it is still the most popular single-byte character encoding scheme in use today. A funny thing about Latin1 encoding is that it maps every byte from 0 to 255 to a valid character. This means that literally any sequence of bytes can be interpreted as a valid string. The main drawback is that it only supports characters from Western European languages. The same is not true for UTF8. Unlike Latin1, UTF8 supports a vastly broader range of characters from different languages and scripts. But as a consequence, not every byte sequence is valid. This fact is due to UTF8's added complexity, using multi-byte sequences for characters beyond the general ASCII range. This is also why you can't just throw any sequence of bytes at it and ex...
Today I learned James Garfield, who once worked as a lawyer, Civil War General, and served as the 20th President of the United States, was math savvy and published a novel Pythagorean theorem proof. [1] \[ \text{Area}_{\text{trapezoid } ACED} = \frac{1}{2} \cdot (AC + DE) \cdot CE = \frac{1}{2} \cdot (a + b) \cdot (a + b) = \frac{(a + b)^2}{2} \] \[ \begin{aligned} \text{Area}_{\text{trapezoid } ACED} &= \text{Area}_{\Delta ACB} + \text{Area}_{\Delta ABD} + \text{Area}_{\Delta BDE} \\ &= \frac{1}{2}(a \times b) + \frac{1}{2}(c \times c) + \frac{1}{2}(a \times b) \end{aligned} \] \[ (a + b) \times \frac{1}{2}(a + b) = \frac{1}{2}(a \times b) + \frac{1}{2}(c \times c) + \frac{1}{2}(a \times b) \] \[ a^{2} + b^{2} = c^{2} \] Small Pieces We can take this in smaller pieces. First, we can find the area of the right-angled trapezoid with the following equation: \[ \text{Area}_{\text{trapezoid}} = \frac{1}{2} \cdot (a + b) \cdot (a + b) = \frac{(a + b)^2}{2} \] We...