Scan and Solve with PhotoMath

PhotoMath is a new app which allows users to scan a math expressions or equations using a phone camera in real time and solve them. As of this writing, the supported expressions/equations are the arithmetic operations (+, -, ×,÷), fractions, decimals, powers and roots, linear equations, powers and roots, quadratic equations, simple systems of linear equations. It also supports absolute value equations and inequalities. Below is a short introductory video about PhotoMath. PhotoMath from MicroBLINK on Vimeo. PhotoMath is available as an iOS, Android, Amazon and Windows Phone application.

Why the Area of a Rhombus is Half the Product of its Diagonals

A rhombus is a parallelogram with four congruent sides. Since it is a parallelogram, it has also all the properties of a parallelogram. One of these properties is that the diagonals bisect each other. That is, they divide each other into two equal parts.

Another property of a rhombus is that the diagonals are perpendicular. So, summarizing all the properties above, if we have rhombus ABCD, then,

\overline{AB} \cong \overline{BC} \cong \overline{CD} \cong \overline{DA}.

and

\overline{AC} \perp \overline{BD}. Continue reading

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