science around us

Limits

I used to tutor calculus. People really struggle with limits and asymptotes. Asymptotes occur where your function is approaching either positive or negative infinity. This happens when the function is “undefined”.

Gradient Field

To help us visualize 3D functions, there are methods to bring the function down a dimension to give you a little taste of how it’s behaving. One of these methods is gradient fields.

Cortical Connections

The cortex of a human brain is complicated. It’s broken into 6 layers, of which several are broken down further into sublayers. Layer 4 receives primary input from lower brain areas.

Joint Probability

A and B are two separate events, but not necessarily completely separate. Sometimes A and B can happen together. The probability of that occurring is given by \(P(A \cap B)\): the joint probability.

Arc Length

Math is everywhere. Here, the wilted shrub forms an arc. Draw a triangle with the tangent line as the hypotenuse, \(\Delta x\) as the base, and \(\Delta y\) as the height.

Area

Finding the area under one curve involves taking the integral of that curve over the interval of interest: \(\int_{a}^{b}{f(x)dx}\). If you want to find the area between two curves ($f(x)$ and \(g(x)\)), you start by taking the integral of the top curve and subtract from that the un-wanted area - the area under the bottom curve.

Center Surround

The back of your retina is lined with light-sensitive rods and cones. These photoreceptors catch the light and send the light information to bipolar cells, who then send it to retinal ganglion cells (RGCs).