Read the following passage about and mark the letter A, B, C, D on your answer sheet to indicate thebest answer to each of the following questions from 31 to 40.

Some people look at an equation and see a bunch of complicated numbers and symbols while otherssee beauty[I]. Now, thanks to a new tool created at Carnegie Mellon University, anyone can now translatethe abstractions of mathematics into beautiful and instructive illustrations[II]. This exciting new tool isnamed Penrose after the mathematician Roger Penrose, who is famous for using diagrams and otherdrawings to communicate complicated mathematical ideas[III]. Penrose enables users to create diagramssimply by typing mathematical expressions and letting the software do the drawing[IV].

Unlike a graphing calculator, these aren’t restricted to basic functions, but can be complexrelationships from any area of mathematics. “Some mathematicians have a talent for drawing beautifuldiagrams by hand, but they vanish as soon as the chalkboard is erased,” said Keenan Crane, an assistantprofessor of computer science and robotics. “We want to make this expressive power available to anyone.”

Diagrams are often underused in mathematical communication, since producing high-qualityillustrations is beyond the skill of many researchers and requires a great deal of time and effort. Penroseaddresses these challenges by letting diagram-drawing experts turn their knowledge about creatingdiagrams into computer codes so that other users can access this capability using familiar mathematicallanguage and a computer. “We started off by asking: ‘How do people translate mathematical ideas intopictures in their head?’” said Katherine Ye, a Ph.D. student in the Computer Science Department who isinvolved in the development of Penrose. “The secret sauce of our system is to empower people to easily‘explain’ this translation process to the computer, so the computer can do all the hard work of actuallymaking the picture.”

Once the computer learns how the user wants to see a mathematical object visualized – a vectorrepresented by a little arrow, for instance, or a point represented as a dot – it uses these rules to draw severalcandidate diagrams. Users can then select and edit the diagrams they want from a gallery ofpossibilities. A special, simple-to-learn programming language was also developed so that they can easilyconvey the ideas in their minds to the Penrose system, Crane said. “Mathematicians can get very pickyabout notations,” he explained. “We let them define whatever notation they want, so they can expressthemselves naturally.”

The researchers will present Penrose at the SIGGRAPH 2020 Conference on Computer Graphicsand Interactive Techniques, which will be held this July. “Our vision is to be able to dust off an old mathtextbook from the library, drop it into the computer and get a beautifully illustrated book - that way morepeople understand,” Crane said, noting that Penrose is a first step toward this goal.

(Adapted from sciencedaily.com)

Actually, (3) ______ of the country’s policies