I studied the language documentation for let rec (1), but did not find anything helpful. It did not seem to say anything about the kind of expressions allowed, or not allowed, to be the right hand side of let rec.
Actually, the manual contains a very precise specification of what is allowed in the right hand side of let rec (this documentation is linked from the page that you looked at, but perhaps it should be made to stand out more):
In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.
The various right- and left-hand rules arise from the fact the three axes of three-dimensional space have two possible orientations. This can be seen by holding your hands together with palms up and fingers curled. If the curl of the fingers represents a movement from the first or x-axis to the second or y-axis, then the third or z-axis can point along either right thumb or left thumb.
The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dimensions. William Rowan Hamilton, recognized for his development of quaternions, a mathematical system for representing three-dimensional rotations, is often attributed with the introduction of this convention. In the context of quaternions, the Hamiltonian product of two vector quaternions yields a quaternion comprising both scalar and vector components.[1] Josiah Willard Gibbs recognized that treating these components separately, as dot and cross product, simplifies vector formalism. Following a substantial debate, [2] the mainstream shifted from Hamilton's quaternionic system to Gibbs' three-vectors system. This transition led to the prevalent adoption of the right-hand rule in the contemporary contexts.
The right-hand rule in physics was introduced in the late 19th century by John Fleming in his book Magnets and Electric Currents.[4] Fleming described the orientation of the induced electromotive force by referencing the motion of the conductor and the direction of the magnetic field in the following depiction: If a conductor, represented by the middle finger, be moved in a field of magnetic flux, the direction of which is represented by the direction of the forefinger, the direction of this motion, being in the direction of the thumb, then the electromotive force set up in it will be indicated by the direction in which the middle finger points."[4]
For right-handed coordinates, if the thumb of a person's right hand points along the z-axis in the positive direction (third coordinate vector), then the fingers curl from the positive x-axis (first coordinate vector) toward the positive y-axis (second coordinate vector). When viewed at a position along the positive z-axis, the turn from the positive x- to the positive y-axis is counter-clockwise.
Interchanging the labels of any two axes reverses the handedness. Reversing the direction of one axis (or three axes) also reverses the handedness. Reversing two axes amounts to a 180 rotation around the remaining axis, also preserving the handedness. These operations can be composed to give repeated changes of handedness.[5] (If the axes do not have a positive or negative direction, then handedness has no meaning.)
In mathematics, a rotating body is commonly represented by a pseudovector along the axis of rotation. The length of the vector gives the speed of rotation and the direction of the axis gives the direction of rotation according to the right-hand rule: right fingers curled in the direction of rotation and the right thumb pointing in the positive direction of the axis. This allows some simple calculations using the vector cross-product. No part of the body is moving in the direction of the axis arrow. If the thumb is pointing north, Earth rotates according to the right-hand rule (prograde motion). This causes the Sun, Moon, and stars to appear to revolve westward according to the left-hand rule.
A helix is a curved line formed by a point rotating around a center while the center moves up or down the z-axis. Helices are either right or left handed with curled fingers giving the direction of rotation and thumb giving the direction of advance along the z-axis.
The threads of a screw are helical and therefore screws can be right- or left-handed. To properly fasten or unfasten a screw, one applies the above rules: if a screw is right-handed, pointing one's right thumb in the direction of the hole and turning in the direction of the right hand's curled fingers (i.e. clockwise) will fasten the screw, while pointing away from the hole and turning in the new direction (i.e. counterclockwise) will unfasten the screw.
In vector calculus, it is necessary to relate a normal vector of a surface to the boundary curve of the surface. Given a surface S with a specified normal direction n̂ (a choice of "upward direction" with respect to S), the boundary curve C around S is defined to be positively oriented provided that the right thumb points in the direction of n̂ and the fingers curl along the orientation of the bounding curve C.
Ampère's right-hand grip rule,[6] also called the right-hand screw rule, coffee-mug rule or the corkscrew-rule; is used either when a vector (such as the Euler vector) must be defined to represent the rotation of a body, a magnetic field, or a fluid, or vice versa, when it is necessary to define a rotation vector to understand how rotation occurs. It reveals a connection between the current and the magnetic field lines in the magnetic field that the current created. Ampère was inspired by fellow physicist Hans Christian Ørsted, who observed that needles swirled when in the proximity of an electric current-carrying wire and concluded that electricity could create magnetic fields.
The right-hand rule has widespread use in physics. A list of physical quantities whose directions are related by the right-hand rule is given below. (Some of these are related only indirectly to cross products, and use the second form.)
Unlike most mathematical concepts, the meaning of a right-handed coordinate system cannot be expressed in terms of any mathematical axioms. Rather, the definition depends on chiral phenomena in the physical world, for example the culturally transmitted meaning of right and left hands, a majority human population with dominant right hand, or certain phenomena involving the weak force.
@JTynes the way I get to that customization spot is by clicking into a Deal. Then click on the gear icon (Settings) in the upper right corner by your profile icon. Then go to the Record Customization tab. Is this what you're looking for?
There is a related request in the HubSpot Ideas section about this, some users have asked to remove or turn off default sections: Customize what information is shown on information cards on right sidebar
I have an update for your here: Customizing the right record sidebar sections is currently a BETA feature, according to HubSpot support it should be available to Professional and Enterprise customers shortly. You can find the documentation here: -setup/customize-record-right-sidebar
Hi I was wondering if it's possible to remove this menu on the right-hand side of course home pages (see image attached). We don't need it as we're not using this as an actual course, but rather as a 'community' of modules that students can dip in and out of. Apart from it not being necessary,it also squishes up the home page and the banner at the top making things look a bit weird - so we'd rather that menu weren't there. Does anyone know of a way to remove it?
Brains trust, can someone explain why the firewall has been designed without bi-lateral symmetry? If the goal is to make Aptera available to right-hand drive markets, why not make the firewall ready to accept the change?
Recently, it has been reported that grasping with the left hand is more vulnerable to visual size illusions than grasping with the right hand. The present study investigated whether this increased sensitivity of the left hand for visual context extends to reaching. Left- and right-handed participants reached for targets embedded in two different visual contexts with either left or right hands. Visual context was manipulated by presenting targets either in a blank field or within an array of placeholders marking possible target locations. Regardless of handedness, the presence of placeholders affected left hand, but not right hand, reaching by improving end-point accuracy and reducing movement speed. Furthermore, left hand reaching was more accurate for far than near targets, whereas right hand reaching showed the opposite pattern. We discuss two possible hemispheric lateralization accounts of these findings.
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