## Understanding angle-distance relation with a visual exploration

Observational Skill 1 – Understanding angle-distance relation with a visual exploration

Observational skill is one of the essential aspects of scientific temperament or approach that makes anyone gather more information. More information leads to get more relations thereby improving the analytical skills and in turn making the person best at understanding the situation or concept.At zerosciencelab, we prioritise providing as many situations or Observables as possible through the technology (backed by a research team)  in the form of interactive virtual activities coupled with some queries to enhance the student’s Observational skills.

Let us consider a situation where a person is walking towards a wall of height (h) from a distance (s). Many of us might have experienced such a situation at some point in time. Have you ever paid attention to how does the wall appear as we move closer to the wall? Don’t you feel the increase in the height of the wall as you move closer and closer to the wall? Is it real? or why does it appear as if the height of the wall increased? What matters? Can we measure the heights of such Objects from distances? Let’s try to understand such a situation through the following interactive activities. Use them to Observe, think, question, create and measure.

Look at the following interactive to understand the concept of angle and its usefulness in knowing the heights and distances. Attempt the quiz following the activity to estimate your understanding.

Did you make the correct guesses? Eager to verify, why not? We suggest stopping the box from moving by clicking the button stop on the right, Change the view by using the tool “Rotate 3D Graphics View” provided on the top bar. Observe, think question how the lines ZI and IN are changing. Look at the variation of the angle formed between the lines ZI and IN.

# Math Visualization with points

A general Polynomial function of degree 4 is given below.

We explore all the possible polynomial functions up to the 4th degree using the tool given below the equation. Here in this tool, we plot the graph of a polynomial by selecting the coefficients.

A polynomial of degree 1 is called a linear polynomial and to get we select a=b=c=0 and vary “d” and “e” and the respective plot is drawn in the graphing area of the tool. from the graph, we can observe the variation of the x-intercept with “d” and “e” variation.

This way one can easily understand the geometrical meaning of different polynomials and find their solutions

## Challenge

Look at the following graphs of polynomial functions. Try to find the appropriate polynomial function for each of the figure given below. This can be achieved with the tool given above. Share your experience in comments